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A spectral algorithm for large-scale systems of nonlinear monotone equations

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Abstract

A derivative-free iterative scheme that uses the residual vector as search direction for solving large-scale systems of nonlinear monotone equations is presented. It is closely related to two recently proposed spectral residual methods for nonlinear systems which use a nonmonotone line-search globalization strategy and a step-size based on the Barzilai-Borwein choice. The global convergence analysis is presented. In order to study the numerical behavior of the algorithm, it is included an extensive series of numerical experiments. Our computational experiments show that the new algorithm is computationally efficient.

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Acknowledgements

We are grateful to two anonymous referees for many suggestions which greatly improved the quality and presentation of this paper.

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Authors and Affiliations

  1. Departamento de Electrónica, Computación y Control, Facultad de Ingeniería, Universidad Central de Venezuela, Caracas, 1053, Venezuela

    William La Cruz

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  1. William La Cruz
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Correspondence to William La Cruz.

Additional information

The work was supported by CDCH-UCV project PG-08-8628-2013/2.

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Cruz, W.L. A spectral algorithm for large-scale systems of nonlinear monotone equations. Numer Algor 76, 1109–1130 (2017). https://doi.org/10.1007/s11075-017-0299-8

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