Estimators for spectral norm of difference form differnt types of matrices $A$ and $B$ . Approximation of the form $\lVert A-B \rVert_2$ or $\lVert A-B \rVert_2$ with some factorized matrix $B$ or $\lVert I - B^{-1} A \rVert_2$ with some facotized matrix $B$ can be computed. More...

Functions
real	norm2diff_amatrix_rkmatrix (pcrkmatrix a, pcamatrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_amatrix_sparsematrix (pcsparsematrix a, pcamatrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_amatrix_hmatrix (pchmatrix a, pcamatrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_amatrix_h2matrix (pch2matrix a, pcamatrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_amatrix_dh2matrix (pcdh2matrix a, pcamatrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_rkmatrix_sparsematrix (pcsparsematrix a, pcrkmatrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_rkmatrix_hmatrix (pchmatrix a, pcrkmatrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_rkmatrix_h2matrix (pch2matrix a, pcrkmatrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_rkmatrix_dh2matrix (pcdh2matrix a, pcrkmatrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_sparsematrix_hmatrix (pchmatrix a, pcsparsematrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_sparsematrix_h2matrix (pch2matrix a, pcsparsematrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_sparsematrix_dh2matrix (pcdh2matrix a, pcsparsematrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_hmatrix_h2matrix (pch2matrix a, pchmatrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_hmatrix_dh2matrix (pcdh2matrix a, pchmatrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_h2matrix_dh2matrix (pcdh2matrix a, pch2matrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

real	norm2diff_lr_amatrix (pcamatrix A, pcamatrix LR)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_lr_amatrix_hmatrix (pcamatrix A, pchmatrix LR)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_chol_amatrix (pcamatrix A, pcamatrix chol)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_chol_amatrix_hmatrix (pcamatrix A, pchmatrix chol)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_lr_hmatrix_amatrix (pchmatrix A, pcamatrix LR)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_lr_hmatrix (pchmatrix A, pchmatrix LR)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_chol_hmatrix_amatrix (pchmatrix A, pcamatrix chol)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_chol_hmatrix (pchmatrix A, pchmatrix chol)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_lr_sparsematrix_amatrix (pcsparsematrix A, pcamatrix LR)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_lr_sparsematrix_hmatrix (pcsparsematrix A, pchmatrix LR)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_chol_sparsematrix_amatrix (pcsparsematrix A, pcamatrix chol)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_chol_sparsematrix_hmatrix (pcsparsematrix A, pchmatrix chol)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_lr_h2matrix_amatrix (pch2matrix A, pcamatrix LR)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_lr_h2matrix_hmatrix (pch2matrix A, pchmatrix LR)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_chol_h2matrix_amatrix (pch2matrix A, pcamatrix chol)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_chol_h2matrix_hmatrix (pch2matrix A, pchmatrix chol)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_lr_dh2matrix_amatrix (pcdh2matrix A, pcamatrix LR)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_lr_dh2matrix_hmatrix (pcdh2matrix A, pchmatrix LR)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_chol_dh2matrix_amatrix (pcdh2matrix A, pcamatrix chol)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_chol_dh2matrix_hmatrix (pcdh2matrix A, pchmatrix chol)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_id_lr_amatrix (pcamatrix A, pcamatrix LR)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_id_lr_amatrix_hmatrix (pcamatrix A, pchmatrix LR)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_id_chol_amatrix (pcamatrix A, pcamatrix chol)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_id_chol_amatrix_hmatrix (pcamatrix A, pchmatrix chol)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_id_lr_hmatrix_amatrix (pchmatrix A, pcamatrix LR)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_id_lr_hmatrix (pchmatrix A, pchmatrix LR)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_id_chol_hmatrix_amatrix (pchmatrix A, pcamatrix chol)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_id_chol_hmatrix (pchmatrix A, pchmatrix chol)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_id_lr_sparsematrix_amatrix (pcsparsematrix A, pcamatrix LR)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_id_lr_sparsematrix_hmatrix (pcsparsematrix A, pchmatrix LR)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_id_chol_sparsematrix_amatrix (pcsparsematrix A, pcamatrix chol)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_id_chol_sparsematrix_hmatrix (pcsparsematrix A, pchmatrix chol)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_id_lr_h2matrix_amatrix (pch2matrix A, pcamatrix LR)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_id_lr_h2matrix_hmatrix (pch2matrix A, pchmatrix LR)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_id_chol_h2matrix_amatrix (pch2matrix A, pcamatrix chol)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_id_chol_h2matrix_hmatrix (pch2matrix A, pchmatrix chol)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_id_lr_dh2matrix_amatrix (pcdh2matrix A, pcamatrix LR)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_id_lr_dh2matrix_hmatrix (pcdh2matrix A, pchmatrix LR)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a LR factorization and can be applied to some vector. More...

real	norm2diff_id_chol_dh2matrix_amatrix (pcdh2matrix A, pcamatrix chol)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

real	norm2diff_id_chol_dh2matrix_hmatrix (pcdh2matrix A, pchmatrix chol)
	Approximate the spectral norm $\\|I - B^{-1}A\\|_2$ . The matrix is given as a Cholesky factorization and can be applied to some vector. More...

Detailed Description

Estimators for spectral norm of difference form differnt types of matrices $A$ and $B$ . Approximation of the form $\lVert A-B \rVert_2$ or $\lVert A-B \rVert_2$ with some factorized matrix $B$ or $\lVert I - B^{-1} A \rVert_2$ with some facotized matrix $B$ can be computed.

Function Documentation

real norm2diff_amatrix_dh2matrix	(	pcdh2matrix	a,
		pcamatrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	D $\mathcal H^2$ matrix .
b	Dense matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_amatrix_h2matrix	(	pch2matrix	a,
		pcamatrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	$\mathcal H^2$ matrix .
b	Dense matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_amatrix_hmatrix	(	pchmatrix	a,
		pcamatrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	Hierarchical matrix .
b	Dense matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_amatrix_rkmatrix	(	pcrkmatrix	a,
		pcamatrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	Low rank matrix .
b	Dense matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_amatrix_sparsematrix	(	pcsparsematrix	a,
		pcamatrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	Sparse matrix .
b	Dense matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_chol_amatrix	(	pcamatrix	A,
		pcamatrix	chol
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	Dense matrix .
chol	Dense Cholesky factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_chol_amatrix_hmatrix	(	pcamatrix	A,
		pchmatrix	chol
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	Dense matrix .
chol	Hierarchical Cholesky factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_chol_dh2matrix_amatrix	(	pcdh2matrix	A,
		pcamatrix	chol
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	D $\mathcal H^2$ matrix .
chol	Dense Cholesky factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_chol_dh2matrix_hmatrix	(	pcdh2matrix	A,
		pchmatrix	chol
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	D $\mathcal H^2$ matrix .
chol	Hierarchical Cholesky factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_chol_h2matrix_amatrix	(	pch2matrix	A,
		pcamatrix	chol
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	$\mathcal H^2$ matrix .
chol	Dense Cholesky factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_chol_h2matrix_hmatrix	(	pch2matrix	A,
		pchmatrix	chol
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	$\mathcal H^2$ matrix .
chol	Hierarchical Cholesky factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_chol_hmatrix	(	pchmatrix	A,
		pchmatrix	chol
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	Hierarchical matrix .
chol	Hierarchical Cholesky factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_chol_hmatrix_amatrix	(	pchmatrix	A,
		pcamatrix	chol
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	Hierarchical matrix .
chol	Dense Cholesky factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_chol_sparsematrix_amatrix	(	pcsparsematrix	A,
		pcamatrix	chol
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	Sparse matrix .
chol	Dense Cholesky factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_chol_sparsematrix_hmatrix	(	pcsparsematrix	A,
		pchmatrix	chol
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	Sparse matrix .
chol	Hierarchical Cholesky factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_h2matrix_dh2matrix	(	pcdh2matrix	a,
		pch2matrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	D $\mathcal H^2$ matrix .
b	$\mathcal H^2$ matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_hmatrix_dh2matrix	(	pcdh2matrix	a,
		pchmatrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	D $\mathcal H^2$ matrix .
b	Hierarchical matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_hmatrix_h2matrix	(	pch2matrix	a,
		pchmatrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	$\mathcal H^2$ matrix .
b	Hierarchical matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_id_chol_amatrix	(	pcamatrix	A,
		pcamatrix	chol
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	Dense matrix .
chol	Dense Cholesky factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_chol_amatrix_hmatrix	(	pcamatrix	A,
		pchmatrix	chol
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	Dense matrix .
chol	Hierarchical Cholesky factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_chol_dh2matrix_amatrix	(	pcdh2matrix	A,
		pcamatrix	chol
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	D $\mathcal H^2$ matrix .
chol	Dense Cholesky factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_chol_dh2matrix_hmatrix	(	pcdh2matrix	A,
		pchmatrix	chol
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	D $\mathcal H^2$ matrix .
chol	Hierarchical Cholesky factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_chol_h2matrix_amatrix	(	pch2matrix	A,
		pcamatrix	chol
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	$\mathcal H^2$ matrix .
chol	Dense Cholesky factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_chol_h2matrix_hmatrix	(	pch2matrix	A,
		pchmatrix	chol
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	$\mathcal H^2$ matrix .
chol	Hierarchical Cholesky factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_chol_hmatrix	(	pchmatrix	A,
		pchmatrix	chol
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	Hierarchical matrix .
chol	Hierarchical Cholesky factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_chol_hmatrix_amatrix	(	pchmatrix	A,
		pcamatrix	chol
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	Hierarchical matrix .
chol	Dense Cholesky factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_chol_sparsematrix_amatrix	(	pcsparsematrix	A,
		pcamatrix	chol
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	Sparse matrix .
chol	Dense Cholesky factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_chol_sparsematrix_hmatrix	(	pcsparsematrix	A,
		pchmatrix	chol
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a Cholesky factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a Cholesky decomposition of $A$ .

Parameters

A	Sparse matrix .
chol	Hierarchical Cholesky factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_lr_amatrix	(	pcamatrix	A,
		pcamatrix	LR
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	Dense matrix .
LR	Dense LR factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_lr_amatrix_hmatrix	(	pcamatrix	A,
		pchmatrix	LR
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	Dense matrix .
LR	Hierarchical LR factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_lr_dh2matrix_amatrix	(	pcdh2matrix	A,
		pcamatrix	LR
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	D $\mathcal H^2$ matrix .
LR	Dense LR factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_lr_dh2matrix_hmatrix	(	pcdh2matrix	A,
		pchmatrix	LR
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	D $\mathcal H^2$ matrix .
LR	Hierarchical LR factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_lr_h2matrix_amatrix	(	pch2matrix	A,
		pcamatrix	LR
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	$\mathcal H^2$ matrix .
LR	Dense LR factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_lr_h2matrix_hmatrix	(	pch2matrix	A,
		pchmatrix	LR
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	$\mathcal H^2$ matrix .
LR	Hierarchical LR factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_lr_hmatrix	(	pchmatrix	A,
		pchmatrix	LR
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	Hierarchical matrix .
LR	Hierarchical LR factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_lr_hmatrix_amatrix	(	pchmatrix	A,
		pcamatrix	LR
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	Hierarchical matrix .
LR	Dense LR factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_lr_sparsematrix_amatrix	(	pcsparsematrix	A,
		pcamatrix	LR
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	Sparse matrix .
LR	Dense LR factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_id_lr_sparsematrix_hmatrix	(	pcsparsematrix	A,
		pchmatrix	LR
	)

Approximate the spectral norm $\|I - B^{-1}A\|_2$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(I - B^{-1}A)^* (I - B^{-1}A)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	Sparse matrix .
LR	Hierarchical LR factorization of the matrix .

Returns: Approximation of $\|I - B^{-1}A\|_2$ .

real norm2diff_lr_amatrix	(	pcamatrix	A,
		pcamatrix	LR
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	Dense matrix .
LR	Dense LR factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_lr_amatrix_hmatrix	(	pcamatrix	A,
		pchmatrix	LR
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	Dense matrix .
LR	Hierarchical LR factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_lr_dh2matrix_amatrix	(	pcdh2matrix	A,
		pcamatrix	LR
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	D $\mathcal H^2$ matrix .
LR	Dense LR factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_lr_dh2matrix_hmatrix	(	pcdh2matrix	A,
		pchmatrix	LR
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	D $\mathcal H^2$ matrix .
LR	Hierarchical LR factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_lr_h2matrix_amatrix	(	pch2matrix	A,
		pcamatrix	LR
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	$\mathcal H^2$ matrix .
LR	Dense LR factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_lr_h2matrix_hmatrix	(	pch2matrix	A,
		pchmatrix	LR
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	$\mathcal H^2$ matrix .
LR	Hierarchical LR factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_lr_hmatrix	(	pchmatrix	A,
		pchmatrix	LR
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	Hierarchical matrix .
LR	Hierarchical LR factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_lr_hmatrix_amatrix	(	pchmatrix	A,
		pcamatrix	LR
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	Hierarchical matrix .
LR	Dense LR factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_lr_sparsematrix_amatrix	(	pcsparsematrix	A,
		pcamatrix	LR
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	Sparse matrix .
LR	Dense LR factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_lr_sparsematrix_hmatrix	(	pcsparsematrix	A,
		pchmatrix	LR
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ . The matrix $B$ is given as a LR factorization and can be applied to some vector.

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation. $B$ is given as a LR decomposition of $A$ .

Parameters

A	Sparse matrix .
LR	Hierarchical LR factorization of the matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_rkmatrix_dh2matrix	(	pcdh2matrix	a,
		pcrkmatrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	D $\mathcal H^2$ matrix .
b	Low rank matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_rkmatrix_h2matrix	(	pch2matrix	a,
		pcrkmatrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	$\mathcal H^2$ matrix .
b	Low rank matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_rkmatrix_hmatrix	(	pchmatrix	a,
		pcrkmatrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	Hierarchical matrix .
b	Low rank matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_rkmatrix_sparsematrix	(	pcsparsematrix	a,
		pcrkmatrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	Sparse matrix .
b	Low rank matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_sparsematrix_dh2matrix	(	pcdh2matrix	a,
		pcsparsematrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	D $\mathcal H^2$ matrix .
b	Sparse matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_sparsematrix_h2matrix	(	pch2matrix	a,
		pcsparsematrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	$\mathcal H^2$ matrix .
b	Sparse matrix .

Returns: Approximation of $\|A-B\|_2$ .

real norm2diff_sparsematrix_hmatrix	(	pchmatrix	a,
		pcsparsematrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	Hierarchical matrix .
b	Sparse matrix .

Returns: Approximation of $\|A-B\|_2$ .

Functions

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