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

arXiv: https://arxiv.org/abs/1812.02056 · HTML: https://mlsanity.com/paper/1812.02056/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2018.

## Built on by (most cited first, 1 of 1)

- [Formal Verification of Unknown Dynamical Systems via Gaussian Process Regression](https://mlsanity.com/paper/2201.00655/) (2021)

## Abstract (arXiv)

This note presents fast Cholesky/LU/QR decomposition algorithms with O(n2.529) 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.