Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm
Mathematical Software
2009-05-18 v5
Abstract
We propose several new schedules for Strassen-Winograd's matrix multiplication algorithm, they reduce the extra memory allocation requirements by three different means: by introducing a few pre-additions, by overwriting the input matrices, or by using a first recursive level of classical multiplication. In particular, we show two fully in-place schedules: one having the same number of operations, if the input matrices can be overwritten; the other one, slightly increasing the constant of the leading term of the complexity, if the input matrices are read-only. Many of these schedules have been found by an implementation of an exhaustive search algorithm based on a pebble game.
Cite
@article{arxiv.0707.2347,
title = {Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm},
author = {Brice Boyer and Jean-Guillaume Dumas and Clément Pernet and Wei Zhou},
journal= {arXiv preprint arXiv:0707.2347},
year = {2009}
}