An Elimination Algorithm for the Computation of All Zeros of a System of Multivariate Polynomial Equations
نویسندگان
چکیده
A direct numerical method is proposed for the determination of all isolated zeros of a system of multivariate polynomial equations. By “polynomial combination”, the system is reduced to a special form which may be interpreted as a multiplication table for power products modulo the system. The zeros are then formed from an ordinary eigenvalue problem for the matrix of the multiplication table. Degenerate situations may be handled by perturbing them into general form and reaching the zeros of the unperturbed system via a homotopy method.
منابع مشابه
Inequalities for the polar derivative of a polynomial with $S$-fold zeros at the origin
Let $p(z)$ be a polynomial of degree $n$ and for a complex number $alpha$, let $D_{alpha}p(z)=np(z)+(alpha-z)p'(z)$ denote the polar derivative of the polynomial p(z) with respect to $alpha$. Dewan et al proved that if $p(z)$ has all its zeros in $|z| leq k, (kleq 1),$ with $s$-fold zeros at the origin then for every $alphainmathbb{C}$ with $|alpha|geq k$, begin{align*} max_{|z|=...
متن کاملSymbolic and Numeric Methods for Exploiting Structure in Constructing Resultant Matrices
Resultants characterize the existence of roots of systems of multivariate nonlinear poly nomial equations while their matrices reduce the computation of all common zeros to a problem in linear algebra Sparse elimination theory has introduced the sparse resul tant which takes into account the sparse structure of the polynomials The construction of sparse resultant or Newton matrices is the criti...
متن کاملNumerical solution of a system of fuzzy polynomial equations by modified Adomian decomposition method
In this paper, we present some efficient numerical algorithm for solving system of fuzzy polynomial equations based on Newton's method. The modified Adomian decomposition method is applied to construct the numerical algorithms. Some numerical illustrations are given to show the efficiency of algorithms.
متن کاملSolving Single Phase Fluid Flow Instability Equations Using Chebyshev Tau- QZ Polynomial
In this article the instability of single phase flow in a circular pipe from laminar to turbulence regime has been investigated. To this end, after finding boundary conditions and equation related to instability of flow in cylindrical coordination system, which is called eigenvalue Orr Sommerfeld equation, the solution method for these equation has been investigated. In this article Chebyshev p...
متن کاملOn the Complexity of Sparse Elimination
Sparse elimination exploits the structure of a set of multivariate polynomials by measuring complexity in terms of Newton polytopes. We examine polynomial systems that generate 0-dimensional ideals: a generic monomial basis for the coordinate ring of such a system is de ned from a mixed subdivision. We o er a simple proof of this known fact and relate the computation of a monomial basis to the ...
متن کامل