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In linear algebra, the Strassen algorithm, named after Volker Strassen, is an algorithm for matrix multiplication. It is faster than the standard matrix multiplication algorithm for large matrices, with a better asymptotic complexity , although the naive algorithm is often better for smaller matrices.
Strassen's algorithm improves on naive matrix multiplication through a divide-and-conquer approach. The key observation is that multiplying two 2 × 2 matrices can be done with only 7 multiplications, instead of the usual 8 (at the expense of 11 additional addition and subtraction operations).
The first to be discovered was Strassen's algorithm, devised by Volker Strassen in 1969 and often referred to as "fast matrix multiplication". It is based on a way of multiplying two 2 × 2 -matrices which require only 7 multiplications (instead of the usual 8), at the expense of several additional addition and subtraction operations.
Matrix multiplication shares some properties with usual multiplication. However, matrix multiplication is not defined if the number of columns of the first factor differs from the number of rows of the second factor, and it is non-commutative, [10] even when the product remains defined after changing the order of the factors. [11] [12]
Volker Strassen (born April 29, 1936) is a German mathematician, a professor emeritus in the department of mathematics and statistics at the University of Konstanz. [1]For important contributions to the analysis of algorithms he has received many awards, including the Cantor medal, [2] the Konrad Zuse Medal, [3] the Paris Kanellakis Award for work on randomized primality testing, [4] the Knuth ...
The Schönhage–Strassen algorithm is based on the fast Fourier transform (FFT) method of integer multiplication. This figure demonstrates multiplying 1234 × 5678 = 7006652 using the simple FFT method. Base 10 is used in place of base 2 w for illustrative purposes. Schönhage (on the right) and Strassen (on the left) playing chess in ...
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
Matrix multiplication algorithm; C. Cannon's algorithm; F. Freivalds' algorithm; S. Strassen algorithm This page was last edited on 3 January 2023, at 17:02 ...