A Distributed Approach for Solving Systems of Nonlinear Equations

Abstract

Solving a system of nonlinear equations is a common operation in many practical applications such as analyzing physics experiments or running simulations of analog electronic circuits. Applications become more and more complex, both in terms of variables and number of involved equations, severely limiting the applicability of the sequential algorithms. As both the processing power and the available bandwidth in modern network increase, the distributing solution becomes more and more appealing. This paper presents a parallel algorithm for solving systems nonlinear of equations based on the Newton-Raphson method. The core of this algorithm is the Gaussian reduction. Our implementation attempts to minimize the overall amount of data to be transferred during both the Gauss pivoting operation and each Newton-Raphson iteration.