A solution to certain polynomial equations with applications to nonlinear fitting

A solution to certain polynomial equations with applications to nonlinear fitting

We present a combinatorial method for solving a certain system of polynomial equations of Vandermonde type in 2N variables by reducing it to the problem of solving two special linear systems of size N and rooting a single univariate polynomial of degree N . Over C, all solutions can be found with fixed precision using, up to polylogarithmic factors, O(N2) bitwise operations in the worst case. F...

A New Strategy for Training RBF Network with Applications to Nonlinear Integral Equations

A new learning strategy is proposed for training of radial basis functions (RBF) network. We apply two different local optimization methods to update the output weights in training process, the gradient method and a combination of the gradient and Newton methods. Numerical results obtained in solving nonlinear integral equations show the excellent performance of the combined gradient method in ...

A New Approach to the Numerical Solution of Dual Fully Fuzzy Polynomial Equations

A new approach to the numerical solution of system of dual fuzzy polynomial equations

Polynomial Fitting of Data Streams with Applications to Codeword Testing

Given a stream of (x, y) points, we consider the problem of finding univariate polynomials that best fit the data. Over finite fields, this problem encompasses the well-studied problem of decoding Reed-Solomon codes while over the reals it corresponds to the well-studied polynomial regression problem. We present one-pass algorithms for two natural problems: i) find the polynomial of a given deg...