Convergence of the Eberlein diagonalization method under the generalized serial pivot strategies

TL;DR

This paper proves the global convergence of the Eberlein diagonalization method for eigenvalue problems under a broad class of pivot strategies, including permutations, and supports findings with numerical examples.

Contribution

It extends the convergence analysis of the Eberlein method to generalized serial pivot strategies, broadening its theoretical applicability.

Findings

Proves global convergence under generalized serial pivot strategies

Includes numerical examples demonstrating the method's effectiveness

Broadens understanding of pivot strategies in eigenvalue algorithms

Abstract

The Eberlein method is a Jacobi-type process for solving the eigenvalue problem of an arbitrary matrix. In each iteration two transformations are applied on the underlying matrix, a plane rotation and a non-unitary elementary transformation. The paper studies the method under the broad class of generalized serial pivot strategies. We prove the global convergence of the Eberlein method under the generalized serial pivot strategies with permutations and present several numerical examples.