Triangular systolic arrays for matrix product and factorisation

Abstract

Triangular systolic arrays for performing the matrix product C = AB and LU triangular matrix factorisation of 2 n∗n matrices A and B with bandwidths w1 w2 respectivelyand w=p+q – 1 are derived using the properties of reflection and refraction of systolic wavefronts. When compared with the hexagonally connected arrays of Kung and Leiserson [1] these new arrays have an efficiency of e = 2/3 rather than 1/3, and for w≈w (product)p≈q (factorisation) save approximately half the number of cells whilst maintaining the same computation time where .