Randomized Krylov-Schur eigensolver with deflation

TL;DR

This paper presents a new randomized Krylov-Schur algorithm for efficiently computing selected eigenpairs of large matrices, featuring simple implementation, deflation, and demonstrated scalability and accuracy.

Contribution

The paper introduces a novel randomized Krylov-Schur eigensolver with deflation, improving efficiency and scalability for large-scale eigenvalue problems.

Findings

Demonstrates scalability on large matrices

Achieves accurate eigenpair computation

Efficient low-dimensional operations

Abstract

This work introduces a novel algorithm to solve large-scale eigenvalue problems and seek a small set of eigenpairs. The method, called randomized Krylov-Schur (rKS), has a simple implementation and benefits from fast and efficient operations in low-dimensional spaces, such as sketch-orthogonalization processes and stable reordering of Schur factorizations. It also includes a practical deflation technique for converged eigenpairs, enabling the computation of the eigenspace associated with a given part of the spectrum. Numerical experiments are provided to demonstrate the scalability and accuracy of the method.