KSPChebyshevEstEigSet#

Automatically estimate the eigenvalues to use for Chebyshev

Synopsis#

#include "petscksp.h" 
PetscErrorCode KSPChebyshevEstEigSet(KSP ksp, PetscReal a, PetscReal b, PetscReal c, PetscReal d)

Logically Collective

Input Parameters#

ksp - the Krylov space context
a - multiple of min eigenvalue estimate to use for min Chebyshev bound (or PETSC_DECIDE)
b - multiple of max eigenvalue estimate to use for min Chebyshev bound (or PETSC_DECIDE)
c - multiple of min eigenvalue estimate to use for max Chebyshev bound (or PETSC_DECIDE)
d - multiple of max eigenvalue estimate to use for max Chebyshev bound (or PETSC_DECIDE)

Options Database Key#

-ksp_chebyshev_esteig a,b,c,d - estimate eigenvalues using a Krylov method, then use this transform for Chebyshev eigenvalue bounds

Notes#

The Chebyshev bounds are set using

   minbound = a*minest + b*maxest
   maxbound = c*minest + d*maxest

The default configuration targets the upper part of the spectrum for use as a multigrid smoother, so only the maximum eigenvalue estimate is used. The minimum eigenvalue estimate obtained by Krylov iteration is typically not accurate until the method has converged.

If 0.0 is passed for all transform arguments (a,b,c,d), eigenvalue estimation is disabled.

The default transform is (0,0.1; 0,1.1) which targets the “upper” part of the spectrum, as desirable for use with multigrid.

The eigenvalues are estimated using the Lanczo (KSPCG) or Arnoldi (KSPGMRES) process using a noisy right hand side vector.