How can we speed up matrix multiplication?
SIAM Review
Algorithms: their complexity and efficiency (2nd ed.)
Algorithms: their complexity and efficiency (2nd ed.)
Superoptimizer: a look at the smallest program
ASPLOS II Proceedings of the second international conference on Architectual support for programming languages and operating systems
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A practical method for code generation based on exhaustive search
SIGPLAN '82 Proceedings of the 1982 SIGPLAN symposium on Compiler construction
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A number of “tricks” are known that trade multiplications for additions. The term “tricks” reflects the way these methods seem not to proceed from any general theory, but instead jump into existence as recipes that work. The Strassen method for 2 by 2 matrix product with 7 multiplications is a well-known example, as is the method for finding a complex number product in 3 multiplications. We have created a practical computer program for finding such tricks automatically, where massive parallelism makes the combinatorially explosive search tolerable for small problems. One result of this program is a method for computing cross products of 3-vectors using only 5 multiplications.