Volume 63, pp. 83-128, 2025.

Global and quadratic convergence of the Block Jacobi method for Hermitian matrices under the de Rijk pivot strategy

Vjeran Hari

Abstract

This paper provides a proof of global and quadratic convergence of the block Jacobi method for Hermitian matrices under the de Rijk pivot strategy. Also global and quadratic convergence of the element-wise Jacobi method under the same pivot strategy is proved. It is shown that sharp quadratic convergence bounds can be deduced from an estimate that is obtained in the global convergence proof. Numerical tests illustrate the behavior of the methods under the de Rijk pivot strategy.

Full Text (PDF) [829 KB], BibTeX , DOI: 10.1553/etna_vol63s83

Key words

eigenvalue problem, block Jacobi method, de Rijk pivot strategy, global convergence, quadratic convergence

AMS subject classifications

65F15

Links to the cited ETNA articles

[30]	Vol. 46 (2017), pp. 107-147 Vjeran Hari and Erna Begović Kovač: Convergence of the cyclic and quasi-cyclic block Jacobi methods