Abstract:We propose a more accurate variant of an algorithm for multiplying 4x4 matrices using 48 multiplications over any ring containing an inverse of 2. This algorithm achieves an error bound exponent of only $\log_{4}gamma_{\infty,2}\approx{2.335}$. In practice, it also reaches a better accuracy w.r.t. max-norm, when compared to previously known such fast algorithms. Furthermore, we propose a straight line program of this algorithm, giving a leading constant in its complexity bound of $\frac{316}{32}n^{2+\log_{4}{3}}+o(n^{2+\log_{4}{3}})$ operations over any ring containing an inverse of 2.
From: Jean-Guillaume Dumas [view email] [via CCSD proxy]
[v1]
Thu, 19 Mar 2026 09:58:19 UTC (34 KB)
[v2]
Mon, 27 Jul 2026 09:13:07 UTC (53 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。