Solving nonlinear systems of equations via spectral residual methods: stepsize selection and applications

Enrico Meli; Benedetta Morini; Margherita Porcelli; Cristina Sgattoni

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arXiv · 2005.05851

Solving nonlinear systems of equations via spectral residual methods: stepsize selection and applications

Enrico Meli·Benedetta Morini·Margherita Porcelli·Cristina Sgattoni

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Abstract

Spectral residual methods are derivative-free and low-cost per iteration procedures for solving nonlinear systems of equations. They are generally coupled with a nonmonotone linesearch strategy and compare well with Newton-based methods for large nonlinear systems and sequences of nonlinear systems. The residual vector is used as the search direction and choosing the steplength has a crucial impact on the performance. In this work we address both theoretically and experimentally the steplength selection and provide results on a real application such as a rolling contact problem.

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Enrico Meli, Benedetta Morini, Margherita Porcelli, Cristina Sgattoni. 2020-05-12. Solving nonlinear systems of equations via spectral residual methods: stepsize selection and applications. https://arxiv.org/abs/2005.05851

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