Spectra  1.0.0 Header-only C++ Library for Large Scale Eigenvalue Problems
Spectra::SymGEigsShiftSolver< OpType, BOpType, Mode > Class Template Reference

#include <Spectra/SymGEigsShiftSolver.h>

## Detailed Description

### template<typename OpType, typename BOpType, GEigsMode Mode> class Spectra::SymGEigsShiftSolver< OpType, BOpType, Mode >

This class implements the generalized eigen solver for real symmetric matrices, i.e., to solve $$Ax=\lambda Bx$$ where $$A$$ and $$B$$ are symmetric matrices. A spectral transform is applied to seek interior generalized eigenvalues with respect to some shift $$\sigma$$.

There are different modes of this solver, specified by the template parameter Mode. See the pages for the specialized classes for details.

• The shift-and-invert mode transforms the problem into $$(A-\sigma B)^{-1}Bx=\nu x$$, where $$\nu=1/(\lambda-\sigma)$$. This mode assumes that $$B$$ is positive definite. See SymGEigsShiftSolver (Shift-and-invert mode) for more details.
• The buckling mode transforms the problem into $$(A-\sigma B)^{-1}Ax=\nu x$$, where $$\nu=\lambda/(\lambda-\sigma)$$. This mode assumes that $$A$$ is positive definite. See SymGEigsShiftSolver (Buckling mode) for more details.
• The Cayley mode transforms the problem into $$(A-\sigma B)^{-1}(A+\sigma B)x=\nu x$$, where $$\nu=(\lambda+\sigma)/(\lambda-\sigma)$$. This mode assumes that $$B$$ is positive definite. See SymGEigsShiftSolver (Cayley mode) for more details.

Definition at line 44 of file SymGEigsShiftSolver.h.

The documentation for this class was generated from the following file: