slepc-main 2024-11-09
DSTranslateRKS
Computes a modification of the dense system corresponding to an update of the shift in a rational Krylov method.
Synopsis
#include "slepcds.h"
PetscErrorCode DSTranslateRKS(DS ds,PetscScalar alpha)
Logically Collective
Input Parameters
| ds | - the direct solver context
|
| alpha | - the translation amount
|
Notes
This function is intended for use in the context of Krylov methods only.
It takes the leading (k+1,k) submatrix of A, containing the truncated
Rayleigh quotient of a Krylov-Schur relation computed from a shift
sigma1 and transforms it to obtain a Krylov relation as if computed
from a different shift sigma2. The new matrix is computed as
1.0/alpha*(eye(k)-Q*inv(R)), where [Q,R]=qr(eye(k)-alpha*A) and
alpha = sigma1-sigma2.
Matrix Q is placed in DS_MAT_Q so that it can be used to update the
Krylov basis.
See Also
DSTranslateHarmonic()
Level
developer
Location
src/sys/classes/ds/interface/dsops.c
Index of all DS routines
Table of Contents for all manual pages
Index of all manual pages