A functional program for Gaussian Elimination

Abstract

This paper has been written as a contribution to the Dutch Parallel Reduction Machine Project. The paper is second in a sequence of papers that gives functional presentations for fundamental algorithms. The aim is to verify experimentally the following claim by functional programmers [BvL]: functional programming is good for writing structured software; better than the so-called imperative von Neumann-languages. In this paper the traditional algorithm of Gaussian Elimination of a system of n linear equations in n indeterminates is presented as a functional program in Miranda. First we will discuss appropriate candidates for the type of matrices and the type of arbitrary n-dimensional arrays, then we give the functional algorithm for Gaussian Elimination.