Parallel implementations of Riemannian conjugate gradient methods for joint approximate diagonalization

Nela Bosner

Vol. 30 No. 1 (2025)

Regular Articles

Parallel implementations of Riemannian conjugate gradient methods for joint approximate diagonalization

Published 2025-03-11

Nela Bosner

Nela Bosner
Department of Mathematics, Faculty of Science, University of Zagreb

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Abstract

We propose multi-threaded parallel implementations of the Riemannian conjugate gradient method (CG) on the Stiefel manifold and on the oblique manifold, suitable for solving two forms of the joint approximate diagonalization problem. In our implementations each fundamental step of the method is explicitly modified and parallelized to enhance computational efficiency. Numerical experiments demonstrate that our modified CG implementations are more efficient than the original versions.

Keywords

joint approximate diagonalization, Riemannian conjugate gradient method, matrix manifolds, parallel implementations, efficient algorithms

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Supplementary File(s)

mc_5356_RAR mc_5356_TEX

Author Biography

Nela Bosner

Department of Mathematics, associate professor