Spectral residual method without gradient information for solving large-scale nonlinear systems of equations
By William La Cruz, Jose Mario Martínez, Marcos Raydan. Mathematics of Computation, 2006
346 citations recorded by the source corpus.
A fully derivative-free spectral residual method for solving largescale 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 largescale problems is also presented.
Subfields: Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/403bcc202522c33755cd70286b3e8ddeee8aadfb
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In Numerical Analysis
Citations in the corpus
- A Modified Fletcher–Reeves Conjugate Gradient Method for Monotone Nonlinear Equations with Some Applications (2019, neutral): “Problem 4 [35] Strictly Convex Function I.”
- Spectral gradient projection method for monotone nonlinear equations with convex constraints (2009, background): “Recently, La Cruz and Raydan [11] extended the spectral approach to nonlinear systems of equations; and later this idea was further extended and analyzed by La Cruz, Mart́ınez and Raydan [12] to explore simultaneously the residual and the minus residual direction (±F (xk)) as possible search directi”