Gomes-Ruggiero, Márcia A.; Martínez, José Mario; Moretti, Antonio Carlos Comparing algorithms for solving sparse nonlinear systems of equations. (English) Zbl 0752.65039 SIAM J. Sci. Stat. Comput. 13, No. 2, 459-483 (1992). This paper presents a numerical comparison of eight algorithms: Newton’s method, Broyden’s first method, Schubert’s method, the Dennis-Marwil method, and three methods of Martínez’s family (the diagonal-scaling method, the row-scaling method and column-scaling method) as applied to solving large sparse nonlinear systems of equations.A survey of convergence results concerning these methods, of various stopping criteria and restarting criteria as well as strategies for singularity and step control is given. Aspects of global implementation of these methods are also examined. Finally, numerical experiments both with local and global algorithms are reported. Reviewer: O.Vaarmann (Tallinn) Cited in 47 Documents MSC: 65H10 Numerical computation of solutions to systems of equations 65K05 Numerical mathematical programming methods Keywords:numerical comparison; algorithms; Newton’s method; Broyden’s first method; Schubert’s method; Dennis-Marwil method; diagonal-scaling method; row-scaling method; column-scaling method; large sparse nonlinear systems; convergence; stopping criteria; restarting criteria; step control; numerical experiments Software:PITCON PDFBibTeX XMLCite \textit{M. A. Gomes-Ruggiero} et al., SIAM J. Sci. Stat. Comput. 13, No. 2, 459--483 (1992; Zbl 0752.65039) Full Text: DOI