Generalized Chebyshev acceleration on the unit disc

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.