Convergence Analysis of Shift-Inverse Method with Richardson Iteration For Eigenvalue Problem

TL;DR

This paper analyzes the convergence behavior of the shift-inverse method combined with Richardson iteration for eigenvalue problems, emphasizing the impact of eigenvalue gaps on convergence speed.

Contribution

It provides a theoretical analysis of how eigenvalue gaps influence the convergence rate of the combined shift-inverse and Richardson iteration method.

Findings

Convergence speed is heavily influenced by the eigenvalue gap.

The analysis clarifies conditions for faster convergence.

Eigenvalue separation is critical for method efficiency.

Abstract

In this paper, we consider the shift-inverse method with Richardson iteration step for the eigenvalue problems. It will be shown that the convergence speed depends heavily on the eigenvalue gap between the desired eigenvalue and undesired ones.