Modelling Iterative Roots of Mappings in Multidimensional Spaces


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lkindermann [ at ] awi-bremerhaven.de

Abstract

Solutions g(x) of the functional equation g(g(x)) = f(x) are called iterative roots of the given function f(x). They are of interest in dynamical systems, chaos and complexity theory and also in the modelling of certain industrial and financial processes. The problem of computing this "square root" in function (or operator) spaces remains a hard task and is, for the general case, still unsolved. While the theory of functional equations provides some insight for realand complex valued functions, iterative roots of mappingsfrom Rn to Rn are not well understood by theory and there exists no published numerical algorithm for their computation. Here we prove existence of iterative roots of a certain class of monotonic mappings in Rn spaces and demonstratehow a method based on neural networks can find solutions to some examples that arise from simple physical systems.



Item Type
Conference (Conference paper)
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Not peer-reviewed
Publication Status
Published
Event Details
Proceedings of the 9th International Conference on Neural Information Processing (ICONIP'02), Singapore.
Eprint ID
10415
Cite as
Kindermann, L. and Georgiev, P. (2002): Modelling Iterative Roots of Mappings in Multidimensional Spaces , Proceedings of the 9th International Conference on Neural Information Processing (ICONIP'02), Singapore .


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