slepc-3.21.0 2024-03-30

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.

Level

developer

Location