We take a fundamental set of matrix functions to be:

Abstract: We present an overview of vectorization techniques for matrix algebra on the G4 Velocity Engine. Though small matrices can be processed above gigaflop rates, our main emphasis herein is on very large matrices, for which the class of Strassen algorithms having superior asymptotic complexity apply. These large-matrix recursions use, as is natural, the very fast, small-matrix core multiply at recursion bottom. We invstigate the matrix operations of: multiplication, inversion, transposition; with a view to appropriate implementation variants with respect to G4 architecture. For N × N matrix operands and 500 MHz. G4, performance results are as follows. For sizes N ∼ 32 one can achieve well over 1 gigaflop/s for the core matrix multiply. For N ∼ 2500 the combination of G4 and Strassen algorithm effects a full multiply in only 40 seconds. For such very-large matrices the Strassen algorithm is 7 times faster than the classical one. In fact the classical-Strassen breakover, though highly dependent on various conditions as we quantify, lies approximately at matrix size N × N = 128 × 128