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 \(\sigma_1\) and transforms it to obtain a Krylov relation as if computed from a different shift \(\sigma_2\). The new matrix is computed as \(\alpha^{-1}(I-QR^{-1})\), where \(QR=I-\alpha A\) and \(\alpha = \sigma_1-\sigma_2\).

Matrix \(Q\) is placed in DS_MAT_Q so that it can be used to update the Krylov basis.