Maximal Volume Matrix Cross Approximation for Image Compression and Least Squares Solution
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915079218266112 |
|---|---|
| author | Allen, Kenneth Lai, Ming-Jun Shen, Zhaiming |
| author_facet | Allen, Kenneth Lai, Ming-Jun Shen, Zhaiming |
| contents | We study the classic matrix cross approximation based on the maximal volume submatrices. Our main results consist of an improvement of the classic estimate for matrix cross approximation and a greedy approach for finding the maximal volume submatrices. More precisely, we present a new proof of the classic estimate of the inequality with an improved constant. Also, we present a family of greedy maximal volume algorithms to improve the computational efficiency of matrix cross approximation. The proposed algorithms are shown to have theoretical guarantees of convergence. Finally, we present two applications: image compression and the least squares approximation of continuous functions. Our numerical results at the end of the paper demonstrate the effective performance of our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_17403 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Maximal Volume Matrix Cross Approximation for Image Compression and Least Squares Solution Allen, Kenneth Lai, Ming-Jun Shen, Zhaiming Numerical Analysis Machine Learning We study the classic matrix cross approximation based on the maximal volume submatrices. Our main results consist of an improvement of the classic estimate for matrix cross approximation and a greedy approach for finding the maximal volume submatrices. More precisely, we present a new proof of the classic estimate of the inequality with an improved constant. Also, we present a family of greedy maximal volume algorithms to improve the computational efficiency of matrix cross approximation. The proposed algorithms are shown to have theoretical guarantees of convergence. Finally, we present two applications: image compression and the least squares approximation of continuous functions. Our numerical results at the end of the paper demonstrate the effective performance of our approach. |
| title | Maximal Volume Matrix Cross Approximation for Image Compression and Least Squares Solution |
| topic | Numerical Analysis Machine Learning |
| url | https://arxiv.org/abs/2309.17403 |