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
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