slepc-main 2024-11-09
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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 = ||A*v-sigma*u||_2 and n2 = ||A^T*u-sigma*v||_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^2*A'*u-c*B'*B*x||_2 and n2 = ||c^2*B'*v-s*A'*A*x||_2, where [u;v] are the left singular vectors and x is the right singular vector, with sigma=c/s.

See Also

SVDErrorType, SVDSolve()

Level

beginner

Location

src/svd/interface/svdsolve.c

Examples

src/svd/tutorials/ex15.c
src/svd/tutorials/ex15f.F90
src/svd/tutorials/ex45.c


Index of all SVD routines
Table of Contents for all manual pages
Index of all manual pages