A Numerical Study on Large-Scale Nonlinear Solvers

We consider the solution of several nonlinear systems that come from the discretization of two-dimensional boundary value problems using well-known algorithms based on the quasi-Newton idea: Newton 's method, Broyden's method and the Column-Updating method. Numerical results can be useful for researchers to indicate the performances that should be improved by future algorithms or implementations. Key words. Nonlinear systems, quasi-Newton methods, Newton's method, globalization. 1 Introduction In this numerical study, we compare Newton and quasi-Newton methods using a simple globalization strategy, based on monotone decrease of the Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970 Campinas SP, Brazil ([email protected]). This work was supported by FAPESP (Grant 90-3724-6), FINEP and FAEP-UNICAMP. Present address of D. N. Kozakevich: Departmento of Mathematics, Federal University of Santa Catarina, Florian'opolis, Santa Catarina, Braz..