A new aggregation technique for the solution of large systems of algebraic equations (IC simulation)

Abstract

The term aggregation denotes a class of methods that were originally conceived as a way to compute an approximate solution of a linear system of equations. It has been shown that they could be used to accelerate the convergence of linear relaxation algorithms. Although all aggregation methods rely on the same general idea, each individual method is usually based on a heuristic that is valid for a particular class of problems. It is shown how the idea behind these methods can be generalized to include nonlinear equations, and a number of theorems concerning their theoretical properties are proven. How their performance in the linear case can be significantly improved if the heuristic approach is abandoned in favor of a rigorously mathematical one is shown. As a practical test, numerical results obtained on a number of matrices resulting from common problems in computer-aided design of integrated circuits are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>