Any admissible harmonic Ritz value set is possible for prescribed GMRES residual norms

TL;DR

This paper proves that for any given set of harmonic Ritz values, there exists a GMRES residual norm sequence that corresponds to it, expanding the understanding of GMRES residual behavior.

Contribution

It demonstrates the realizability of any admissible harmonic Ritz value set for prescribed GMRES residual norms, complementing previous theoretical results.

Findings

Any admissible harmonic Ritz value set can be realized with prescribed GMRES residual norms.

The result extends the theoretical understanding of GMRES residual and Ritz value relationships.

Provides a constructive approach for matching Ritz values with residual norms.

Abstract

We show that any admissible harmonic Ritz value set is possible for prescribed GMRES residual norms, which is a complement for the results in [Duintjer Tebbens and Meurant, {\it SIAM J. Matrix Anal. Appl.}, 33 (2012), no. 3, pp. 958--978].