A modified least squares algorithm for solving sparse n × n sets of nonlinear equations

Abstract In this paper we describe an algorithm for solving sparse n × n sets of nonlinear algebraic equations. This algorithm is like the Levenberg-Marquardt algorithm in that at each iteration the step size taken affects the direction selected to search; this direction lies between the Newton and gradient directions. Unlike the Levenberg-Marquardt schemes the sparsity of the original equations is preserved and thus spare matrix methods can be employed for solving the linearized system of equations.