A Modified Version of the Waxman Algorithm

TL;DR

This paper presents a modified version of Waxman's iterative algorithm that enhances convergence for solving eigenvalue problems involving large hermitian matrices, maintaining the original method's simplicity.

Contribution

The authors introduce a novel modification to Waxman's algorithm, significantly improving its convergence rate while preserving its core advantages.

Findings

Enhanced convergence speed demonstrated in numerical experiments

Effective for low-lying eigenpairs of large hermitian matrices

Maintains simplicity and elegance of the original method

Abstract

The iterative algorithm recently proposed by Waxman for solving eigenvalue problems, which relies on the method of moments, has been modified to improve its convergence considerably without sacrificing its benefits or elegance. The suggested modification is based on methods to calculate low-lying eigenpairs of large bounded hermitian operators or matrices.