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

La Cruz, William; Martínez, José; Raydan, Marcos

doi:10.1090/S0025-5718-06-01840-0

Spectral residual method without gradient information for solving large-scale nonlinear systems of equations
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by William La Cruz, José Mario Martínez and Marcos Raydan;

Math. Comp. 75 (2006), 1429-1448

DOI: https://doi.org/10.1090/S0025-5718-06-01840-0

Published electronically: April 11, 2006

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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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