Volume 65, pp. 26-62, 2026.

On convergence and accuracy of the J-Jacobi method under the de Rijk pivot strategy

Vjeran Hari and Vedran Novaković

Abstract

This paper proves global convergence of the elementwise $J$-Jacobi method for $J$-Hermitian matrices under the de Rijk pivot strategy and briefly considers the asymptotic convergence of the method. Also considered is the accuracy of a new code for hyperbolic rotations of order two that employs only correctly rounded operations. The numerical tests demonstrate the advantage in the convergence speed of the $J$-Jacobi method under the de Rijk pivot strategy over the same method under the row-cyclic strategy for both the two-sided and the one-sided (implicit) variant of the method.

Full Text (PDF) [1.4 MB], BibTeX , DOI: 10.1553/etna_vol65s26

Key words

eigenvalue problem, $J$-Jacobi method, de Rijk pivot strategy, global convergence, high relative accuracy, hyperbolic singular value decomposition

AMS subject classifications

65F15

Links to the cited ETNA articles

[19]	Vol. 63 (2025), pp. 83-128 Vjeran Hari: Global and quadratic convergence of the block Jacobi method for Hermitian matrices under the de Rijk pivot strategy
[20]	Vol. 46 (2017), pp. 107-147 Vjeran Hari and Erna Begović Kovač: Convergence of the cyclic and quasi-cyclic block Jacobi methods