H2Lib  3.0
matrixnorms

Estimators for spectral norm of difference form differnt types of matrices and . Approximation of the form or with some factorized matrix or with some facotized matrix can be computed. More...

## Functions

real norm2diff_amatrix_rkmatrix (pcrkmatrix a, pcamatrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_amatrix_sparsematrix (pcsparsematrix a, pcamatrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_amatrix_hmatrix (pchmatrix a, pcamatrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_amatrix_h2matrix (pch2matrix a, pcamatrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_amatrix_dh2matrix (pcdh2matrix a, pcamatrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_rkmatrix_sparsematrix (pcsparsematrix a, pcrkmatrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_rkmatrix_hmatrix (pchmatrix a, pcrkmatrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_rkmatrix_h2matrix (pch2matrix a, pcrkmatrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_rkmatrix_dh2matrix (pcdh2matrix a, pcrkmatrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_sparsematrix_hmatrix (pchmatrix a, pcsparsematrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_sparsematrix_h2matrix (pch2matrix a, pcsparsematrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_sparsematrix_dh2matrix (pcdh2matrix a, pcsparsematrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_hmatrix_h2matrix (pch2matrix a, pchmatrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_hmatrix_dh2matrix (pcdh2matrix a, pchmatrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_h2matrix_dh2matrix (pcdh2matrix a, pch2matrix b)
Approximate the spectral norm of the difference of two matrices and . More...

real norm2diff_lr_amatrix (pcamatrix A, pcamatrix LR)
Approximate the spectral norm 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 . 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 . 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 . 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 . 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 . 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 . 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 . 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 . 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 . 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 . 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 . 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 . 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 . 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 . 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 . 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 . 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 . 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 . 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 . 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 . 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 and . Approximation of the form or with some factorized matrix or with some facotized matrix can be computed.

## Function Documentation

 real norm2diff_amatrix_dh2matrix ( pcdh2matrix a, pcamatrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a D matrix . b Dense matrix .
Returns
Approximation of .
 real norm2diff_amatrix_h2matrix ( pch2matrix a, pcamatrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a matrix . b Dense matrix .
Returns
Approximation of .
 real norm2diff_amatrix_hmatrix ( pchmatrix a, pcamatrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a Hierarchical matrix . b Dense matrix .
Returns
Approximation of .
 real norm2diff_amatrix_rkmatrix ( pcrkmatrix a, pcamatrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a Low rank matrix . b Dense matrix .
Returns
Approximation of .
 real norm2diff_amatrix_sparsematrix ( pcsparsematrix a, pcamatrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a Sparse matrix . b Dense matrix .
Returns
Approximation of .
 real norm2diff_chol_amatrix ( pcamatrix A, pcamatrix chol )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A Dense matrix . chol Dense Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_chol_amatrix_hmatrix ( pcamatrix A, pchmatrix chol )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A Dense matrix . chol Hierarchical Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_chol_dh2matrix_amatrix ( pcdh2matrix A, pcamatrix chol )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A D matrix . chol Dense Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_chol_dh2matrix_hmatrix ( pcdh2matrix A, pchmatrix chol )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A D matrix . chol Hierarchical Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_chol_h2matrix_amatrix ( pch2matrix A, pcamatrix chol )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A matrix . chol Dense Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_chol_h2matrix_hmatrix ( pch2matrix A, pchmatrix chol )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A matrix . chol Hierarchical Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_chol_hmatrix ( pchmatrix A, pchmatrix chol )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A Hierarchical matrix . chol Hierarchical Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_chol_hmatrix_amatrix ( pchmatrix A, pcamatrix chol )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A Hierarchical matrix . chol Dense Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_chol_sparsematrix_amatrix ( pcsparsematrix A, pcamatrix chol )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A Sparse matrix . chol Dense Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_chol_sparsematrix_hmatrix ( pcsparsematrix A, pchmatrix chol )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A Sparse matrix . chol Hierarchical Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_h2matrix_dh2matrix ( pcdh2matrix a, pch2matrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a D matrix . b matrix .
Returns
Approximation of .
 real norm2diff_hmatrix_dh2matrix ( pcdh2matrix a, pchmatrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a D matrix . b Hierarchical matrix .
Returns
Approximation of .
 real norm2diff_hmatrix_h2matrix ( pch2matrix a, pchmatrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a matrix . b Hierarchical matrix .
Returns
Approximation of .
 real norm2diff_id_chol_amatrix ( pcamatrix A, pcamatrix chol )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A Dense matrix . chol Dense Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_chol_amatrix_hmatrix ( pcamatrix A, pchmatrix chol )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A Dense matrix . chol Hierarchical Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_chol_dh2matrix_amatrix ( pcdh2matrix A, pcamatrix chol )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A D matrix . chol Dense Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_chol_dh2matrix_hmatrix ( pcdh2matrix A, pchmatrix chol )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A D matrix . chol Hierarchical Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_chol_h2matrix_amatrix ( pch2matrix A, pcamatrix chol )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A matrix . chol Dense Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_chol_h2matrix_hmatrix ( pch2matrix A, pchmatrix chol )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A matrix . chol Hierarchical Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_chol_hmatrix ( pchmatrix A, pchmatrix chol )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A Hierarchical matrix . chol Hierarchical Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_chol_hmatrix_amatrix ( pchmatrix A, pcamatrix chol )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A Hierarchical matrix . chol Dense Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_chol_sparsematrix_amatrix ( pcsparsematrix A, pcamatrix chol )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A Sparse matrix . chol Dense Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_chol_sparsematrix_hmatrix ( pcsparsematrix A, pchmatrix chol )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a Cholesky decomposition of .

Parameters
 A Sparse matrix . chol Hierarchical Cholesky factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_lr_amatrix ( pcamatrix A, pcamatrix LR )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A Dense matrix . LR Dense LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_lr_amatrix_hmatrix ( pcamatrix A, pchmatrix LR )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A Dense matrix . LR Hierarchical LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_lr_dh2matrix_amatrix ( pcdh2matrix A, pcamatrix LR )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A D matrix . LR Dense LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_lr_dh2matrix_hmatrix ( pcdh2matrix A, pchmatrix LR )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A D matrix . LR Hierarchical LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_lr_h2matrix_amatrix ( pch2matrix A, pcamatrix LR )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A matrix . LR Dense LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_lr_h2matrix_hmatrix ( pch2matrix A, pchmatrix LR )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A matrix . LR Hierarchical LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_lr_hmatrix ( pchmatrix A, pchmatrix LR )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A Hierarchical matrix . LR Hierarchical LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_lr_hmatrix_amatrix ( pchmatrix A, pcamatrix LR )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A Hierarchical matrix . LR Dense LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_lr_sparsematrix_amatrix ( pcsparsematrix A, pcamatrix LR )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A Sparse matrix . LR Dense LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_id_lr_sparsematrix_hmatrix ( pcsparsematrix A, pchmatrix LR )

Approximate the spectral norm . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A Sparse matrix . LR Hierarchical LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_lr_amatrix ( pcamatrix A, pcamatrix LR )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A Dense matrix . LR Dense LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_lr_amatrix_hmatrix ( pcamatrix A, pchmatrix LR )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A Dense matrix . LR Hierarchical LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_lr_dh2matrix_amatrix ( pcdh2matrix A, pcamatrix LR )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A D matrix . LR Dense LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_lr_dh2matrix_hmatrix ( pcdh2matrix A, pchmatrix LR )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A D matrix . LR Hierarchical LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_lr_h2matrix_amatrix ( pch2matrix A, pcamatrix LR )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A matrix . LR Dense LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_lr_h2matrix_hmatrix ( pch2matrix A, pchmatrix LR )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A matrix . LR Hierarchical LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_lr_hmatrix ( pchmatrix A, pchmatrix LR )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A Hierarchical matrix . LR Hierarchical LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_lr_hmatrix_amatrix ( pchmatrix A, pcamatrix LR )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A Hierarchical matrix . LR Dense LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_lr_sparsematrix_amatrix ( pcsparsematrix A, pcamatrix LR )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A Sparse matrix . LR Dense LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_lr_sparsematrix_hmatrix ( pcsparsematrix A, pchmatrix LR )

Approximate the spectral norm of the difference of two matrices and . The matrix 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 and computing the square root of the resulting eigenvalue approximation. is given as a LR decomposition of .

Parameters
 A Sparse matrix . LR Hierarchical LR factorization of the matrix .
Returns
Approximation of .
 real norm2diff_rkmatrix_dh2matrix ( pcdh2matrix a, pcrkmatrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a D matrix . b Low rank matrix .
Returns
Approximation of .
 real norm2diff_rkmatrix_h2matrix ( pch2matrix a, pcrkmatrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a matrix . b Low rank matrix .
Returns
Approximation of .
 real norm2diff_rkmatrix_hmatrix ( pchmatrix a, pcrkmatrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a Hierarchical matrix . b Low rank matrix .
Returns
Approximation of .
 real norm2diff_rkmatrix_sparsematrix ( pcsparsematrix a, pcrkmatrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a Sparse matrix . b Low rank matrix .
Returns
Approximation of .
 real norm2diff_sparsematrix_dh2matrix ( pcdh2matrix a, pcsparsematrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a D matrix . b Sparse matrix .
Returns
Approximation of .
 real norm2diff_sparsematrix_h2matrix ( pch2matrix a, pcsparsematrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a matrix . b Sparse matrix .
Returns
Approximation of .
 real norm2diff_sparsematrix_hmatrix ( pchmatrix a, pcsparsematrix b )

Approximate the spectral norm of the difference of two matrices and .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix and computing the square root of the resulting eigenvalue approximation.

Parameters
 a Hierarchical matrix . b Sparse matrix .
Returns
Approximation of .