Generalized Chebyshev acceleration on the unit disc

TL;DR

This paper introduces a relaxed generalized Chebyshev acceleration method that broadens applicability to matrices with less restrictive eigenvalue conditions, demonstrating effectiveness on large-scale sparse normal matrices.

Contribution

It proposes an alternative iterative scheme that relaxes the eigenvalue inclusion condition required by traditional Chebyshev acceleration.

Findings

Effective acceleration on large-scale sparse normal matrices.

Broader applicability due to relaxed eigenvalue conditions.

Convergence to the same solution as traditional methods.

Abstract

Generalized Chebyshev acceleration is a semi-iterative technique applicable to a basic iterative method only when the eigenvalues of the iteration matrix satisfy a highly restrictive inclusion condition. In this work, we relax this requirement by introducing an alternative iterative scheme that converges to the same solution. The effectiveness of the proposed approach is examined through its application to a large-scale sparse normal matrix.