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

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arxiv 1812.02056 v1 pith:W2LAJHQU submitted 2018-12-05 cs.NA cs.DScs.NA

Cristóbal Camarero This is my paper · ORCID
classification cs.NAcs.DS
keywords algorithmsfastmultiplicationcholeskydecompositionmatrixsimpletime
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abstract

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.

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Cited by 1 Pith paper

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  1. Subspace Selected Variational Quantum Configuration Interaction with a Partial Walsh Series

    quant-ph 2026-01 conditional novelty 6.0 of 10

    A new variational quantum eigensolver ansatz combines subspace-selected superpositions with diagonal Walsh operators to prepare CI wavefunctions, demonstrated on molecules.

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