Joint Approximate Partial Diagonalization of Large Matrices Article Swipe

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YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2409.02005

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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Joint (building) Mathematics Combinatorics Applied mathematics Engineering Structural engineering

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2409.02005
PDF: https://arxiv.org/pdf/2409.02005
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4402955354

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DOI: https://doi.org/10.48550/arxiv.2409.02005

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Title: Joint Approximate Partial Diagonalization of Large Matrices

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-09-03

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Authors: Abd‐Krim Seghouane, Yousef Saad

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Landing page: https://arxiv.org/abs/2409.02005

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PDF URL: https://arxiv.org/pdf/2409.02005

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Concepts: Joint (building), Mathematics, Combinatorics, Applied mathematics, Engineering, Structural engineering

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