Constrained Optimisation of Rational Functions for Accelerating Subspace Iteration
This is an incremental improvement for numerical linear algebra practitioners computing eigenvalues in a given interval.
The paper improves the FEAST algorithm for eigenvalue computation by developing better rational filter functions, achieving up to 25% fewer iterations on average compared to state-of-the-art functions.
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.