KSPLSQRConvergedDefault#
Determines convergence of the KSPLSQR Krylov method, including a check on the residual norm of the normal equations.
Synopsis#
#include "petscksp.h"
PetscErrorCode KSPLSQRConvergedDefault(KSP ksp, PetscInt n, PetscReal rnorm, KSPConvergedReason *reason, void *ctx)
Collective
Input Parameters#
ksp - iterative context
n - iteration number
rnorm - 2-norm residual value (may be estimated)
ctx - convergence context which must have been created by
KSPConvergedDefaultCreate()
Output Parameter#
reason - the convergence reason
Notes#
This is not called directly but rather is passed to KSPSetConvergenceTest(). It is used automatically by KSPLSQR
KSPConvergedDefault() is called first to check for convergence in \(A*x=b\).
If that does not determine convergence then checks convergence for the least squares problem, i.e., in \( \min_x |b - A x| \).
Possible convergence for the least squares problem (which is based on the residual of the normal equations) are KSP_CONVERGED_RTOL_NORMAL_EQUATIONS
and KSP_CONVERGED_ATOL_NORMAL_EQUATIONS.
KSP_CONVERGED_RTOL_NORMAL_EQUATIONS is returned if \(||A^T r|| < rtol ||A|| ||r||\).
The matrix norm \(||A||\) is an iteratively refined estimate, see KSPLSQRGetNorms().
This criterion is largely compatible with that in MATLAB lsqr().
See Also#
KSP: Linear System Solvers, KSPLSQR, KSPSetConvergenceTest(), KSPSetTolerances(), KSPConvergedSkip(), KSPConvergedReason, KSPGetConvergedReason(),
KSPConvergedDefaultSetUIRNorm(), KSPConvergedDefaultSetUMIRNorm(), KSPConvergedDefaultCreate(), KSPConvergedDefaultDestroy(),
KSPConvergedDefault(), KSPLSQRGetNorms(), KSPLSQRSetExactMatNorm()
Level#
advanced
Location#
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages