Optimized solution strategy for solving systems of equations

Abstract

The focus of this paper is the determination of an optimum solution strategy that improves the rate of convergence when solving general systems of equations. Improved convergence is accomplished by using a logic‐based algorithm, which we call logical equation set decomposition (LESD), to decompose large systems into subsets of smaller systems. Our goal is to reduce the computational complexity of solving large equation sets by solving multiple smaller equation subsets. An occurrence matrix is used to optimize the number of subsets as well as the order of solution. Improved convergence rates were verified by integrating LESD into a standard numerical equation solver with a conventional Netwon's method as the numerical engine. Linear and nonlinear equation sets were used to benchmark convergence rate. The results showed orders of magnitude reduction in computational time when using LESD for both linear and nonlinear equation sets.

Citation

Alexander, D.G. and Blackketter, D.M. (2003), "Optimized solution strategy for solving systems of equations", Engineering Computations, Vol. 20 No. 2, pp. 178-191. https://doi.org/10.1108/02644400310465308