SVDComputeError#

Computes the error (based on the residual norm) associated with the i-th singular triplet.

Synopsis#

#include "slepcsvd.h" 
PetscErrorCode SVDComputeError(SVD svd,PetscInt i,SVDErrorType type,PetscReal *error)

Collective

Input Parameters#

svd - the singular value solver context
i - the solution index
type - the type of error to compute

Output Parameter#

error - the error

Notes#

The error can be computed in various ways, all of them based on the residual norm obtained as sqrt(n1^2+n2^2) with n1 = ||Av-sigmau||_2 and n2 = ||A^Tu-sigmav||_2, where sigma is the singular value, u is the left singular vector and v is the right singular vector.

In the case of the GSVD, the two components of the residual norm are n1 = ||s^2A’u-cB’Bx||_2 and n2 = ||c^2B’v-sA’Ax||_2, where [u;v] are the left singular vectors and x is the right singular vector, with sigma=c/s.