English

Simple, Fast and Practicable Algorithms for Cholesky, LU and QR Decomposition Using Fast Rectangular Matrix Multiplication

Numerical Analysis 2018-12-06 v1 Data Structures and Algorithms

Abstract

This note presents fast Cholesky/LU/QR decomposition algorithms with O(n2.529)O(n^{2.529}) time complexity when using the fastest known matrix multiplication. The algorithms have potential application, since a quickly made implementation using Strassen multiplication has lesser execution time than the employed by the GNU Scientific Library for the same task in at least a few examples. The underlaying ideas are very simple. Despite this, I have been unable to find these methods in the literature.

Keywords

Cite

@article{arxiv.1812.02056,
  title  = {Simple, Fast and Practicable Algorithms for Cholesky, LU and QR Decomposition Using Fast Rectangular Matrix Multiplication},
  author = {Cristóbal Camarero},
  journal= {arXiv preprint arXiv:1812.02056},
  year   = {2018}
}
R2 v1 2026-06-23T06:32:50.603Z