Joint Approximate Partial Diagonalization of Large Matrices
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913490814369792 |
|---|---|
| author | Seghouane, Abd-Krim Saad, Yousef |
| author_facet | Seghouane, Abd-Krim Saad, Yousef |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Joint Approximate Partial Diagonalization of Large Matrices Seghouane, Abd-Krim Saad, Yousef Numerical Analysis 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. |
| title | Joint Approximate Partial Diagonalization of Large Matrices |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.02005 |