A constructive approach for finding arbitrary roots of polynomials by neural networks

Authors:
De-Shuang Huang
Affiliations:
Inst. of Intelligent Machines, Chinese Acad. of Sci., Anhui, China
Venue:
IEEE Transactions on Neural Networks
Year:
2004

Citing 0
Cited 21

A neural root finder of polynomials based on root moments

Neural Computation
New conditions for global exponential stability of cellular neural networks with delays

Neural Networks
Neural solution to the target intercept problems in a gun fire control system

Neurocomputing
Modified constrained learning algorithms incorporating additional functional constraints into neural networks

Information Sciences: an International Journal
Neurodynamic Analysis for the Schur Decomposition of the Box Problems

Computational Intelligence and Security
Implementation of Multi-valued Logic Based on Bi-threshold Neural Networks

ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Part II--Advances in Neural Networks
Improved Learning Algorithms of SLFN for Approximating Periodic Function

ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Artificial Intelligence
A generalized-constraint neural network model: Associating partially known relationships for nonlinear regressions

Information Sciences: an International Journal
A novel modular neural network for imbalanced classification problems

Pattern Recognition Letters
Determining the number of real roots of polynomials through neural networks

Computers & Mathematics with Applications
Dynamics of solution for a class of delayed diffusive neural networks with mixed boundary conditions

Neurocomputing
Globally attractive periodic state of discrete-time cellular neural networks with time-varying delays

ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
A new modified hybrid learning algorithm for feedforward neural networks

ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
A new learning algorithm for function approximation incorporating a priori information into extreme learning machine

ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Study of parametric relation in ant colony optimization approach to traveling salesman problem

ICIC'06 Proceedings of the 2006 international conference on Computational Intelligence and Bioinformatics - Volume Part III
Ant colony system for optimizing vehicle routing problem with time windows (VRPTW)

ICIC'06 Proceedings of the 2006 international conference on Computational Intelligence and Bioinformatics - Volume Part III
Methods of decreasing the number of support vectors via k-mean clustering

ICIC'05 Proceedings of the 2005 international conference on Advances in Intelligent Computing - Volume Part I
A recurrent neural network for extreme eigenvalue problem

ICIC'05 Proceedings of the 2005 international conference on Advances in Intelligent Computing - Volume Part I
Improvements to the conventional layer-by-layer BP algorithm

ICIC'05 Proceedings of the 2005 international conference on Advances in Intelligent Computing - Volume Part II
An efficient constrained learning algorithm for stable 2D IIR filter factorization

Advances in Artificial Neural Systems
Application of BW-ELM model on traffic sign recognition

Neurocomputing

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper proposes a constructive approach for finding arbitrary (real or complex) roots of arbitrary (real or complex) polynomials by multilayer perceptron network (MLPN) using constrained learning algorithm (CLA), which encodes the a priori information of constraint relations between root moments and coefficients of a polynomial into the usual BP algorithm (BPA). Moreover, the root moment method (RMM) is also simplified into a recursive version so that the computational complexity can be further decreased, which leads the roots of those higher order polynomials to be readily found. In addition, an adaptive learning parameter with the CLA is also proposed in this paper; an initial weight selection method is also given. Finally, several experimental results show that our proposed neural connectionism approaches, with respect to the nonneural ones, are more efficient and feasible in finding the arbitrary roots of arbitrary polynomials.