Joint Approximate Partial Diagonalization of Large Matrices
Abstract
Given a set of symmetric (real) matrices, the Orthogonal Joint Diagonalization (OJD) problem consists of finding an orthonormal basis in which the representation of each of these 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.
Cite
@article{arxiv.2409.02005,
title = {Joint Approximate Partial Diagonalization of Large Matrices},
author = {Abd-Krim Seghouane and Yousef Saad},
journal= {arXiv preprint arXiv:2409.02005},
year = {2024}
}