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Evolutionary algorithms for computing zeros of nonlinear functions

✍ Scribed by G.A. Tsirogiannis; G.N. Beligiannis; S.D. Likothanassis; M.N. Vrahatis

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
321 KB
Volume
47
Category
Article
ISSN
0362-546X

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✦ Synopsis

A method for locating and computing solutions of systems of nonlinear algebraic and/or transcendental equations or fixed points of continuous functions is described. Our method is based on various well-known notions of Combinatorial Topology and it utilizes evolutionary programming techniques. In particular, the proposed method constructs a Sperner simplex in the (n)-dimensional Euclidean space by applying an evolutionary programming technique. Our method converges rapidly to a solution, independently of the initial guess, and is particularly useful, since it proceeds solely by comparing relative sizes of the function values.

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✍ Florian A. Potra πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 533 KB

We consider two hybrid algorithms for finding an \(\varepsilon\)-approximation of a root of a convex real function that is twice differentiable and satisfies a certain growth condition on the intervial \([0, R]\). The first algorithm combines a binary search procedure with Newton's method. The binar