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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Spectral residual method without gradient information for solving large-scale nonlinear systems of equations


Authors: William La Cruz, José Mario Martínez and Marcos Raydan
Journal: Math. Comp. 75 (2006), 1429-1448
MSC (2000): Primary 49M05, 90C06, 90C56, 65K10
Published electronically: April 11, 2006
MathSciNet review: 2219036
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Abstract: A fully derivative-free spectral residual method for solving large-scale nonlinear systems of equations is presented. It uses in a systematic way the residual vector as a search direction, a spectral steplength that produces a nonmonotone process and a globalization strategy that allows for this nonmonotone behavior. The global convergence analysis of the combined scheme is presented. An extensive set of numerical experiments that indicate that the new combination is competitive and frequently better than well-known Newton-Krylov methods for large-scale problems is also presented.


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Additional Information

William La Cruz
Affiliation: Departamento de Electrónica, Computación y Control, Facultad de Ingeniería, Universidad Central de Venezuela, Caracas 1051-DF, Venezuela
Email: wlacruz@elecrisc.ing.ucv.ve

José Mario Martínez
Affiliation: Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970 Campinas SP, Brazil
Email: martinez@ime.unicamp.br

Marcos Raydan
Affiliation: Departamento de Computación, Facultad de Ciencias, Universidad Central de Vene- zuela, Apartado 47002, Caracas 1041-A, Venezuela
Email: mraydan@kuaimare.ciens.ucv.ve

DOI: http://dx.doi.org/10.1090/S0025-5718-06-01840-0
PII: S 0025-5718(06)01840-0
Keywords: Nonlinear systems, spectral gradient method, nonmonotone line search, Newton-Krylov methods
Received by editor(s): July 14, 2004
Received by editor(s) in revised form: February 1, 2005
Published electronically: April 11, 2006
Additional Notes: The first author was supported by Agenda Petróleo UCV-PROJECT 97-003769.
The second author was supported by PRONEX-Optimization 76.79.1008-00, FAPESP (Grant 2001-04597-4), CNPq and FAEP-UNICAMP
The third author was supported by Agenda Petróleo UCV-PROJECT 97-003769.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.