ACM Transactions on Mathematical Software (TOMS)
Constrained Learning in Neural Networks: Application to Stable Factorization of 2-D Polynomials
Neural Processing Letters
Accelerated Solution of Multivariate Polynomial Systems of Equations
SIAM Journal on Computing
Root Moments: An Alternative Interpretation of Cepstra for Signal Feature Extraction and Modeling
ASILOMAR '95 Proceedings of the 29th Asilomar Conference on Signals, Systems and Computers (2-Volume Set)
FFT-based fast polynomial rooting
ICASSP '00 Proceedings of the Acoustics, Speech, and Signal Processing, 2000. on IEEE International Conference - Volume 06
A constructive approach for finding arbitrary roots of polynomials by neural networks
IEEE Transactions on Neural Networks
An efficient constrained training algorithm for feedforward networks
IEEE Transactions on Neural Networks
Root finding and approximation approaches through neural networks
ACM SIGSAM Bulletin
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
Determining the number of real roots of polynomials through neural networks
Computers & Mathematics with Applications
ICIC'09 Proceedings of the Intelligent computing 5th international conference on Emerging intelligent computing technology and applications
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
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Recognition of leaf images based on shape features using a hypersphere classifier
ICIC'05 Proceedings of the 2005 international conference on Advances in Intelligent Computing - Volume Part I
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
| Hi-index | 0.00 |
This letter proposes a novel neural root finder based on the root moment method (RMM) to find the arbitrary roots (including complex ones) of arbitrary polynomials. This neural root finder (NRF) was designed based on feedforward neural networks (FNN) and trained with a constrained learning algorithm (CLA). Specifically, we have incorporated the a priori information about the root moments of polynomials into the conventional backpropagation algorithm (BPA), to construct a new CLA. The resulting NRF is shown to be able to rapidly estimate the distributions of roots of polynomials. We study and compare the advantage of the RMM-based NRF over the previous root coefficient method-based NRF and the traditional Muller and Laguerre methods as well as the mathematica roots function, and the behaviors, the accuracies of the resulting root finders, and their training speeds of two specific structures corresponding to this FNN root finder: the log Σ and the Σ - Π FNN. We also analyze the effects of the three controlling parameters {δP0, θp,η} with the CLA on the two NRFs theoretically and experimentally. Finally, we present computer simulation results to support our claims.