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Matrix multiplication via arithmetic progressions. (English) Zbl 0702.65046
A new method is presented for accelerating matrix multiplication asymptotically by a basic trilinear form which is not a matrix product. The method is based on Schönhage’s $$\tau$$-theorem, Strassen’s construction, and the Salem-Spencer theorem. The first variant of construction gives a matrix exponent $$\omega =2.404$$. An improvement to of 2.388 is obtained by considering more terms and indices. Finally, some more complicated techniques offer a better estimate of 2.376. A combinatorial construction (whose realization is not guaranteed) is proposed which would yield $$\omega =2$$.
Reviewer: O.Brudaru

##### MSC:
 65F30 Other matrix algorithms (MSC2010) 65Y20 Complexity and performance of numerical algorithms
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##### References:
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