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arXiv · 2409.02005

Joint Approximate Partial Diagonalization of Large Matrices

Abd-Krim Seghouane·Yousef Saad
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Abstract

Given a set of $p$ symmetric (real) matrices, the Orthogonal Joint Diagonalization (OJD) problem consists of finding an orthonormal basis in which the representation of each of these $p$ matrices is as close as possible to a diagonal matrix. We argue that when the matrices are of large dimension, then the natural generalization of this problem is to seek an orthonormal basis of a certain subspace that is a near eigenspace for all the matrices in the set. We refer to this as the problem of ``partial joint diagonalization of matrices.'' The approach proposed first finds this approximate common near eigenspace and then proceeds to a joint diagonalization of the restrictions of the input matrices in this subspace. A few solution methods for this problem are proposed and illustrations of its potential applications are provided.

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Abd-Krim Seghouane, Yousef Saad. 2024-09-03. Joint Approximate Partial Diagonalization of Large Matrices. https://arxiv.org/abs/2409.02005

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