slepc-3.15.0 2021-03-31
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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 on ds

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.

Location: src/sys/classes/ds/interface/dsops.c
Index of all DS routines
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Index of all manual pages