slepc-main 2024-11-22
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BVMatArnoldi

Computes an Arnoldi factorization associated with a matrix.

Synopsis

#include "slepcbv.h"   
PetscErrorCode BVMatArnoldi(BV V,Mat A,Mat H,PetscInt k,PetscInt *m,PetscReal *beta,PetscBool *breakdown)
Collective

Input Parameters

V  - basis vectors context
A  - the matrix
H  - (optional) the upper Hessenberg matrix
k  - number of locked columns
m  - dimension of the Arnoldi basis, may be modified

Output Parameters

beta  - (optional) norm of last vector before normalization
breakdown  - (optional) flag indicating that breakdown occurred

Notes

Computes an m-step Arnoldi factorization for matrix A. The first k columns are assumed to be locked and therefore they are not modified. On exit, the following relation is satisfied

                   A * V - V * H = beta*v_m * e_m^T

where the columns of V are the Arnoldi vectors (which are orthonormal), H is an upper Hessenberg matrix, e_m is the m-th vector of the canonical basis. On exit, beta contains the norm of V[m] before normalization.

The breakdown flag indicates that orthogonalization failed, see BVOrthonormalizeColumn(). In that case, on exit m contains the index of the column that failed.

The values of k and m are not restricted to the active columns of V.

To create an Arnoldi factorization from scratch, set k=0 and make sure the first column contains the normalized initial vector.

See Also

BVMatLanczos(), BVSetActiveColumns(), BVOrthonormalizeColumn()

Level

advanced

Location

src/sys/classes/bv/interface/bvkrylov.c

Index of all BV routines
Table of Contents for all manual pages
Index of all manual pages