Combination of the sequential secant method and Broyden's method with projected updates

Abstract

We introduce a new algorithm for solving nonlinear simultaneous equations, which is a combination of the sequential secant method with Broyden's Quasi-Newton method with projected updates as introduced by Gay and Schnabel. The new algorithm has the order of convergence of the sequential secant method and the choice of the first increments is justified by the minimum variation principles of Quasi-Newton methods. Two versions of the method are compared numerically with some well-known test problems.