Root finding and approximation approaches through neural networks

Authors:
M. G. Epitropakis;M. N. Vrahatis
Affiliations:
University of Patras, Patras, Greece;University of Patras, Patras, Greece
Venue:
ACM SIGSAM Bulletin
Year:
2005

Citing 7
Cited 1

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Abstract

In this paper, we propose two approaches to approximate high order multivariate polynomials and to estimate the number of roots of high order univariate polynomials. We employ high order neural networks such as Ridge Polynomial Networks and Pi -- Sigma Networks, respectively. To train the networks efficiently and effectively, we recommend the application of stochastic global optimization techniques. Finally, we propose a two step neural network based technique, to estimate the number of roots of a high order univariate polynomial.