Subdivision methods for solving polynomial equations

Subdivision methods for solving polynomial equations

This paper presents a new algorithm for solving a system of polynomials, in a domain of . It can be seen as an improvement of the Interval Projected Polyhedron algorithm proposed by Sherbrooke and Patrikalakis [SP93]. It uses a powerful reduction strategy based on univariate root finder using Bernstein basis representation and Descarte’s rule. We analyse the behavior of the method, from a theor...

Non-polynomial Spline Method for Solving Coupled Burgers Equations

In this paper, non-polynomial spline method for solving Coupled Burgers Equations are presented. We take a new spline function. The stability analysis using Von-Neumann technique shows the scheme is unconditionally stable. To test accuracy the error norms 2L, L are computed and give two examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equation...

Symbolic-numeric methods for solving polynomial equations and applications

This tutorial gives an introductive presentation of algebraic and geometric methods for solving a polynomial system f1 = · · · = fm = 0. The first class of methods is based on the study of the quotient algebra A of the polynomial ring modulo the ideal I = (f1, . . . , fm). We show how to deduce the geometry of the solutions, from the structure of A and in particular, how solving polynomial equa...

The Comparison of Numerical Methods for Solving Polynomial Equations

In this paper we compare the Turan process [5]-[6] with the Lehmer-Schur method [2]. We prove that the latter is better. 1. The Algorithms. We first describe the Turan process [5]-[6] which can be considered as an improvement of Graeffe's method. For the complex polynomial (1.1) P0(z)=t «/o*' = ° (fl/o G C, a00an0 * 0), 7=0 the method can be formulated as follows. Let (1.2) Pj(z) = Phx(sfz~)phx...

Solving Polynomial Equations