slepc3.21.1 20240426
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 KrylovSchur 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 = sigma1sigma2.
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