Strassen’s $$2 \times 2$$ matrix multiplication algorithm: a conceptual perspective
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Strassen's 2x2 matrix multiplication algorithm: A conceptual perspective
Despite its importance, all proofs of the correctness of Strassen's famous 1969 algorithm to multiply two 2x2 matrices with only seven multiplications involve some more or less tedious calculations such as explicitly multiplying specific 2x2 matrices, expanding expressions to cancel terms with opposing signs, or expanding tensors over the standard basis. This is why the proof is nontrivial to m...
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There has been much effort to improve the runtime of matrix multiplication. The trivial algorithm multiplies n×n matrices in O(n) time. Strassen (’69) surprised everyone by giving an O(n) time algorithm. This began a long line of improvements until in 1986, Coppersmith and Winograd achieved O(n). After 24 years of no progress, in 2010 Andrew Stothers, a graduate student in Edinburgh, improved t...
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ژورنال
عنوان ژورنال: ANNALI DELL'UNIVERSITA' DI FERRARA
سال: 2019
ISSN: 0430-3202,1827-1510
DOI: 10.1007/s11565-019-00318-1