Constrained Optimisation of Rational Functions for Accelerating Subspace Iteration

TL;DR

This paper advances the FEAST algorithm by developing optimized rational filter functions through constrained minimization, resulting in fewer iterations and improved efficiency in eigenvalue computations.

Contribution

It introduces a novel constrained optimization approach for rational filter functions, enhancing FEAST's performance over existing methods.

Findings

FEAST requires up to 25% fewer iterations with new filters.

New rational filters outperform previous versions in eigenvalue accuracy.

The approach is computationally efficient and broadly applicable.

Abstract

Earlier this decade, the so-called FEAST algorithm was released for computing the eigenvalues of a matrix in a given interval. Previously, rational filter functions have been examined as a parameter of FEAST. In this thesis, we expand on existing work with the following contributions: (i) Obtaining well-performing rational filter functions via standard minimisation algorithms, (ii) Obtaining constrained rational filter functions efficiently, and (iii) Improving existing rational filter functions algorithmically. Using our new rational filter functions, FEAST requires up to one quarter fewer iterations on average compared to state-of-art rational filter functions.