Numerical Solution of Nonlinear Systems of Algebraic Equations

Abstract

Considered in this paper are two basic methods of approximating the solutions of nonlinear systems of algebraic equations. The Steepest Descent method was presented as a way of obtaining good and sufficient initial guess (starting value) which is in turn used for the Broyden's method. Broyden's method on the other hand replaces the Newton's method which requires the use of the inverse of the Jacobian matrix at every new step of iteration with a matrix whose inverse is directly determined at each step by up-dating the previous inverse. The result obtained by this method revealed that the setbacks encountered in computing the inverse of the Jacobian matrix at every step number is eliminated hence saving human effort and computer time. The obtained results also showed that the number of steps that is reduced when compared to Newton's method used on the same problem.