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

Vjeran  Hari; Vedran  Novaković

doi:doi:10.1553/etna_vol65s26

Ronny Ramlau, Lothar Reichel (Hg.)

ETNA - Electronic Transactions on Numerical Analysis

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

Vjeran Hari,

Vedran Novaković

ETNA - Electronic Transactions on Numerical Analysis, pp. 26-62, 2026/02/02

doi: 10.1553/etna_vol65s26

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doi:10.1553/etna_vol65s26

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.

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

ETNA

Published Online: 2026/02/02

Object Identifier: 0xc1aa5572 0x00413377

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Ronny Ramlau, Lothar Reichel (Hg.)

ETNA - Electronic Transactions on Numerical Analysis

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

Abstract