Generalized preconditioned locally harmonic residual method for non-Hermitian eigenproblems

TL;DR

The paper introduces GPLHR, a robust and efficient block iteration method for computing specific eigenvalues of non-Hermitian problems, leveraging preconditioning without requiring shift-invert transformations.

Contribution

It presents a unified framework for standard and generalized eigenproblems, improving robustness and efficiency over existing methods, especially with limited memory.

Findings

GPLHR outperforms existing methods in robustness and efficiency.

The method effectively handles large-scale problems with limited memory.

It does not require exact shift-and-invert transformations.

Abstract

We introduce the Generalized Preconditioned Locally Harmonic Residual (GPLHR) method for solving standard and generalized non-Hermitian eigenproblems. The method is particularly useful for computing a subset of eigenvalues, and their eigen- or Schur vectors, closest to a given shift. The proposed method is based on block iterations and can take advantage of a preconditioner if it is available. It does not need to perform exact shift-and-invert transformation. Standard and generalized eigenproblems are handled in a unified framework. Our numerical experiments demonstrate that GPLHR is generally more robust and efficient than existing methods, especially if the available memory is limited.