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Title:
Fast matrix multiplication
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Abstract:
How many arithmetic operations does it take to multiply two square matrices? This question has captured the imagination of computer scientists ever since Strassen showed in 1969 that \(O(n^{2.81})\) operations suffice. We survey the classical theory of fast matrix multiplication, starting with Strassen's algorithm and culminating with the state-of-the-art Coppersmith-Winograd algorithm and its recent improvements. We also describe Coppersmith's \(O(n^2 log^2 n)\) algorithm for multiplying rectangular matrices, used by Ryan Williams in his separation of ACC and NEXP.
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