Variants of matrix-matrix multiplication for Fortran-90

The Fortran--90 standard requires an intrinsic function matmul which multiplies two matrices together to produce a third as the result. However, the standard does not specify which algorithm to use. We consider an extension to the matmul syntax which allows a Winograd variant of Strassen's algorithm to be added. We discuss an implementation that is in a commercial Fortran--90 offering. Key words. BLAS, matrix multiplication, Winograd's variant of Strassen's algorithm, multilevel algorithms AMS(MOS) subject classification. Numerical Analysis: Numerical Linear Algebra 1 Introduction Fortran--90 [1] has a rich set of intrinsic functions built into it that operate on large objects such as vectors and matrices. We would like to draw attention to the fact that the algorithms that implement these functions are not usually specified in the standard. As a result of this, IBM TM recently added a Winograd variant of Strassen's algorithm in its Fortran--90 compiler, XLF 3.1.1 (the April, 19..