GEMMW: A PORTABLE LEVEL 3 BLAS WINOGRAD VARIANT OF STRASSEN'S MATRIX{MATRIX MULTIPLY ALGORITHM

Abstract. Matrix{matrix multiplication is normally computed using one of the BLAS or a reinvention of part of the BLAS. Unfortunately, the BLAS were designed with small matrices in mind. When huge, well conditioned matrices are multiplied together, the BLAS perform like the blahs, even on vector machines. For matrices where the coe cients are well conditioned, Winograd's variant of Strassen's algorithm o ers some relief, but is rarely available in a quality form on most computers. We reconsider this method and o er a highly portable solution based on the Level 3 BLAS interface. Key Words. Level 3 BLAS, matrix multiplication, Winograd's variant of Strassen's algorithm, multilevel algorithm