The Dilatation Method for the Close Roots of polynomials

摘要

In finding roots of polynomials, ones meet often with the case that two roots are possible very closer so that they can be considered as only one root. In other words, they can not be resolved by some root-finder. This phenomenon is generally prohibited in most cases. In order to solve this problem, this paper proposes a dilation method to change the positions of roots in space so that all roots in space become further and further. As a result, any closer roots can be readily resolved. In this paper, the root-finder based on feedforward neural networks (FNN) trained with constrained learning can be considered to verify our dilation method for eliminating close roots. Finally, some experimental results are presented to support our claim.