ABSTRACT
Matrix multiplication is an important mathematical operation that has extensive applications in numerous research, development, and production areas. Furthermore, matrix multiplication is a building block in performing many other fundamental matrix operations such as computing the powers, characteristic polynomial, determinant, rank, inverse, LU-factorization and QR-factorization of a matrix, and in solving other mathematical problems such as graph theory problems. Owing to its fundamental importance in sciences and engineering, much effort has been devoted to finding and implementing fast matrix multiplication algorithms. Many sequential algorithms have been proposed for matrix multiplication. The standard sequential algorithm has O(N 3) time complexity in multiplying two N ×N matrices. Since Strassen’s remarkable discovery of his O(N 2.8074) algorithm [43], successive progress has been made to
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develop fast sequential matrix multiplication algorithms with time complexity O(N α), where 2 < α < 3. The current best value of α is less than 2.3755 [7].
