Simple, Fast and Practicable Algorithms for Cholesky, LU and QR Decomposition Using Fast Rectangular Matrix Multiplication
It offers faster practical algorithms for fundamental matrix decompositions, potentially benefiting scientific computing applications.
The paper presents fast Cholesky, LU, and QR decomposition algorithms achieving O(n^{2.529}) time complexity using the fastest known matrix multiplication, with a Strassen-based implementation outperforming the GNU Scientific Library in some examples.
This note presents fast Cholesky/LU/QR decomposition algorithms with $O(n^{2.529})$ 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.