From linear to nonlinear iterative methods

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 unconstrain...

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Bibliographic Details
Published inApplied numerical mathematics Vol. 45; no. 1; pp. 59 - 77
Main Authors Vrahatis, M.N., Magoulas, G.D., Plagianakos, V.P.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Amsterdam Elsevier B.V 01.04.2003
Elsevier
Subjects
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Numerical methods in mathematical programming
Numerical methods in mathematical programming, optimization and calculus of variations
Sciences and techniques of general use
Transcendental equation
Convergence of numerical methods
Numerical analysis
Unconstrained optimization
Linear system
Numerical linear algebra
Algebraic equation
Iterative method
Neural network
Non linear system
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Summary: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.
ISSN:0168-9274
1873-5460
DOI:10.1016/S0168-9274(02)00235-0