LSU factorization
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913743601926144 |
|---|---|
| author | Malaschonok, Gennadi |
| author_facet | Malaschonok, Gennadi |
| contents | The matrix LU factorization algorithm is a fundamental algorithm in linear algebra. We propose a generalization of the LU and LEU algorithms to accommodate the case of a commutative domain and its field of quotients. This algorithm decomposes any matrix A into a product of three matrices A=LSU, where each element of the triangular matrices L and U is a minor of matrix A. The number of non-zero elements in matrix S is equal to rank(A), and each of them is the inverse of the product of a specific pair of matrix A minors. The algorithm's complexity is equivalent to that of matrix multiplication. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13640 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | LSU factorization Malaschonok, Gennadi Symbolic Computation Commutative Algebra 15A23 G.1.3 The matrix LU factorization algorithm is a fundamental algorithm in linear algebra. We propose a generalization of the LU and LEU algorithms to accommodate the case of a commutative domain and its field of quotients. This algorithm decomposes any matrix A into a product of three matrices A=LSU, where each element of the triangular matrices L and U is a minor of matrix A. The number of non-zero elements in matrix S is equal to rank(A), and each of them is the inverse of the product of a specific pair of matrix A minors. The algorithm's complexity is equivalent to that of matrix multiplication. |
| title | LSU factorization |
| topic | Symbolic Computation Commutative Algebra 15A23 G.1.3 |
| url | https://arxiv.org/abs/2503.13640 |