Re:On AlphaTensor’s new matrix multiplication algorithms
by bjourne on Saturday October 08, 2022 @12:21PM
(#33133584)
"A considerable group of numerical analysts still believes in the folk “theorem” that fast MM is always numerical unstable, but in actual tests loss of accuracy in fast MM algorithms was limited, and formal proofs of quite reasonable numerical stability of all known fast MM algorithms is available (see [23], [90], [91], [62], and [61])." https://arxiv.org/abs/1804.04102
what good will it do to compute something if its error is unbound?
the issue of the accumulation of roundoff errors is generally speaking unavoidable when it's linear but fortunately they tend to be small