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Applying the Powell's Symmetrical Technique to Conjugate Gradient Methods with the Generalized Conjugacy Condition
(Numerical Functional Analysis and Optimization, 2016-07-02) Noureddine Benrabia, Yamina Laskri, Hamza Guebbai, Mehiddin Al-Baali
This article proposes new conjugate gradient method for unconstrained optimization by applying the Powell symmetrical technique in a defined sense. Using the Wolfe line search conditions, the global convergence property of the method is also obtained based on the spectral analysis of the conjugate gradient iteration matrix and the Zoutendijk condition for steepest descent methods. Preliminary numerical results for a set of 86 unconstrained optimization test problems verify the performance of the algorithm and show that the Generalized Descent Symmetrical Hestenes-Stiefel algorithm is competitive with the Fletcher-Reeves (FR) and Polak-Ribiére-Polyak (PRP+) algorithms.
On the regularization method for Fredholm integral equations with odd weakly singular kernel
(Computational and Applied Mathematics, 2018-03-23) Noureddine Benrabia & Hamza Guebbai
In this paper, we propose a numerical method to approach the solution of a Fredholm integral equation with a weakly singular kernel by applying the convolution product as a regularization operator and the Fourier series as a projection. Preliminary numerical results show that the order of convergence of the method is better than the one of conventional projection methods.