Book Review: Fast Matrix Multiplication with Applications

Abstract.

This book provides an in-depth treatment, including full proofs, of the development of fast matrix multiplication algorithms following the discovery of Strassen’s algorithm or, more precisely, Winograd’s algorithm a year earlier, although the latter cannot be applied recursively. The development is described up to Schönhage’s tau theorem. The author places special emphasis on exact algorithms for multiplying matrices of small formats, which are particularly well suited for designing practically relevant algorithms through recursive application. In addition, the book concludes with a range of applications, such as computing other linear algebra problems in matrix multiplication time.