NEPApplyResolvent#

Applies the resolvent \(T^{-1}(z)\) to a given vector.

Synopsis#

#include "slepcnep.h" 
PetscErrorCode NEPApplyResolvent(NEP nep,RG rg,PetscScalar omega,Vec v,Vec r)

Collective

Input Parameters#

  • nep - the nonlinear eigensolver context

  • rg - optional region

  • omega - value where the resolvent must be evaluated

  • v - input vector

Output Parameter#

  • r - result vector

Note#

The resolvent \(T^{-1}(z) = \sum_i (z-\lambda_i)^{-1} x_i y_i^*\) is evaluated at \(z=\omega\) and the matrix-vector multiplication \(r = T^{-1}(\omega) v\) is computed. Vectors \(x_i\) and \(y_i\) are right and left eigenvectors, respectively, normalized so that \(y_i^*T'(\lambda_i)x_i=1\). The sum contains only eigenvectors that have been previously computed with NEPSolve(), and if a region rg is given then only those corresponding to eigenvalues inside the region are considered.

See Also#

NEP: Nonlinear Eigenvalue Problems, NEPGetLeftEigenvector(), NEPSolve()

Level#

intermediate

Location#

src/nep/interface/nepresolv.c

Examples#

src/nep/tutorials/ex42.c

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