Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm

Details Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm

2007-07-16

arxiv.org/abs/0707.2347v5

(International Symposium on Symbolic and Algebraic Computation 2009), S\'eoul : Cor\'ee, R\'epublique de (2009)

Computer Science

Mathematical Software

Scientific paper

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.

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