Dilation method for finding close roots of polynomials based on constrained learning neural networks

Abstract

In finding roots of polynomials, often two or more roots that are close together in solution space are very difficult to be resolved by a root-finder. To solve this problem, this Letter proposes a dilation method to transform the positions of roots in space so that all roots in space are pulled further apart. As a result, those close (including complex) roots can be readily resolved efficiently by a root-finder. In addition, in this Letter a complex version of constrained learning algorithm is derived. Moreover, our previously proposing feedforward neural network (FNN) root-finder is adopted to address the root finding issue. Finally, some satisfactory results that support our approach are presented.