LSU factorization
Symbolic Computation
2025-03-19 v1 Commutative Algebra
Abstract
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.
Cite
@article{arxiv.2503.13640,
title = {LSU factorization},
author = {Gennadi Malaschonok},
journal= {arXiv preprint arXiv:2503.13640},
year = {2025}
}
Comments
7 pages, 1 figures