Matrix multiplication algorithm

Common card · No. 205368

Because matrix multiplication is such a central operation in many numerical algorithms, much work has been invested in making matrix multiplication algorithms efficient. Applications of matrix multiplication in computational problems are found in many fields including scientific computing and pattern recognition and in seemingly unrelated problems such as counting the paths through a graph. Many different algorithms have been designed for multiplying matrices on different types of hardware, including parallel and distributed systems, where the computational work is spread over multiple processors (perhaps over a network). Directly applying the mathematical definition of matrix multiplication gives an algorithm that takes time on the order of n3 field operations to multiply two n × n matrices over that field (Θ(n3) in big O notation). Better asymptotic bounds on the time required to multiply matrices have been known since the Strassen's algorithm in the 1960s, but the optimal time (that...

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