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2015

Improving the numerical stability of fast matrix multiplication

Ballard, Grey, Benson, Austin R., Druinsky, Alex et al.

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Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest.

Apart from Strassen's original algorithm, few fast algorithms have been efficiently implemented or used in practical applications.
However, there exist many practical alternatives to Strassen's algorithm with varying performance and numerical properties.
Fast algorithms are known to be numerically stable, but because their error bounds are slightly weaker than the classical algorithm, they are not used even in cases where they provide a performance benefit.

Improving the numerical stability of fast matrix multiplication · Around

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A. R. Benson and G. Ballard

2015

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