From linear to nonlinear iterative methods

Authors:
M. N. Vrahatis;G. D. Magoulas;V. P. Plagianakos
Affiliations:
Department of Mathematics, University of Patras, GR-26110 Patras, Greece and University of Patras Artificial Intelligence Research Center (UPAIRC), GR-26110 Patras, Greece;Department of Information Systems and Computing, Brunel University, Uxbridge UB8 3PH, United Kingdom and University of Patras Artificial Intelligence Research Center (UPAIRC), GR-26110 Patras, Gre ...;Department of Mathematics, University of Patras, GR-26110 Patras, Greece and University of Patras Artificial Intelligence Research Center (UPAIRC), GR-26110 Patras, Greece
Venue:
Applied Numerical Mathematics
Year:
2003

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Abstract

This paper constitutes an effort towards the generalization of the most common classical iterative methods used for the solution of linear systems (like Gauss-Seidel, SOR, Jacobi, and others) to the solution of systems of nonlinear algebraic and/or transcendental equations, as well as to unconstrained optimization of nonlinear functions. Convergence and experimental results are presented. The proposed algorithms have also been implemented and tested on classical test problems and on real-life artificial neural network applications and the results to date appear to be very promising.