Determining the number of real roots of polynomials through neural networks

Authors:
B. Mourrain;N. G. Pavlidis;D. K. Tasoulis;M. N. Vrahatis
Affiliations:
-;Computational Intelligence Laboratory (CI Lab), Department of Mathematics University of Patras, GR-26110 Patras, Greece;Computational Intelligence Laboratory (CI Lab), Department of Mathematics University of Patras, GR-26110 Patras, Greece and University of Patras Artificial Intelligence Research Center (UPAIRC), U ...;Computational Intelligence Laboratory (CI Lab), Department of Mathematics University of Patras, GR-26110 Patras, Greece and University of Patras Artificial Intelligence Research Center (UPAIRC), U ...
Venue:
Computers & Mathematics with Applications
Year:
2006

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Abstract

The ability of feedforward neural networks to identify the number of real roots of univariate polynomials is investigated. Furthermore, their ability to determine whether a system of multivariate polynomial equations has real solutions is examined on a problem of determining the structure of a molecule. The obtained experimental results indicate that neural networks are capable of performing this task with high accuracy even when the training set is very small compared to the test set.