Computes a modification of the dense system corresponding to an update of the shift in a rational Krylov method.
PetscErrorCode DSTranslateRKS(DS ds,PetscScalar alpha)
|ds || - the direct solver context
|alpha || - the translation amount
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
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