Systolic implementation of nonlinear transformation of two sequences

This paper concerns with linear bidirectional systolic array (BLSA) since it can be applied for solving a broad class of scientific and technical problems, such as matrix-vector multiplications, eigen value computation, solving systems of linear equations iteratively. This makes this array some kind universal. The array with the same topology, but different functionality of PEs, can be applied for solving problems in operational research, graph theory, discrete mathematics, etc. In this paper we will show how a nonlinear transformation of two given sequences (a/sub 1/,a/sub 2/,...,a/sub n/) and (b/sub 1/,b/sub 2/,... ,b) and matrix W=(w/sub ij/), i=1,2,...,n, j=1,2,...,n, can be computed on BLSA. The transformation can be described as c/sub ij/=w/sub ij//spl oplus/a/sub i//spl odot/b/sub j/, for each i=1,2,...,n and j=1,2,...,n. Binary operations /spl oplus/ and /spl odot/ are closed, associative and commutative. This transformation represents a mathematical model for broad class of problems that are met in operational research, graph theory, discrete mathematics, etc. We illustrate the presentation on the example of finding shortest path in a given graph.