Finding All Isolated Zeros of Polynomial Systems inCnvia Stable Mixed Volumes
نویسندگان
چکیده
منابع مشابه
Simultaneous Methods for Finding All Zeros of a Polynomial
The purpose of this paper is to present three new methods for finding all simple zeros of polynomials simultaneously. First, we give a new method for finding simultaneously all simple zeros of polynomials constructed by applying the Weierstrass method to the zero in the trapezoidal Newton’s method, and prove the convergence of the method. We also present two modified Newton’s methods combined w...
متن کاملSingular Zeros of Polynomial Systems
Singular zeros of systems of polynomial equations constitute a bottleneck when it comes to computing, since several methods relying on the regularity of the Jacobian matrix of the system do not apply when the latter has a non-trivial kernel. Therefore they require special treatment. The algebraic information regarding an isolated singularity can be captured by a finite, local basis of different...
متن کاملOn annuli containing all the zeros of a polynomial
In this paper, we obtain the annuli that contain all the zeros of the polynomial p(z) = a 0 + a 1 z + a 2 z 2 + · · · + a n z n , where a i 's are complex coefficients and z is a complex variable. Our results sharpen some of the recently obtained results in this direction. Also, we develop a MATLAB code to show that for some polynomials the bounds obtained by our results are considerably sharpe...
متن کاملAnnulus containing all the zeros of a polynomial
Recently Dalal and Govil [5] proved that, for any set of positive numbers {Ak}k=1 such that ∑n k=1 Ak = 1, a complex polynomial P (z) = ∑n k=0 dkz k (dk = 0, 0 ≤ k ≤ n) has all its zeros in the annulus A = {z : r1 ≤ |z| ≤ r2}, where r1 = min 1≤k≤n { Ak ∣∣∣d0 dk ∣∣∣ } 1 k and r2 = max 1≤k≤n { 1 Ak ∣∣∣dn−k dn ∣∣∣ } 1 k . This paper presents the best possible results in the same direction by ident...
متن کاملAn Algorithm for Finding All Zeros of Vector Functions
Computing a zero of a continuous function is an old and extensively researched problem in numerical computation. In this paper, we present an efficient subdivision algorithm for finding all real roots of a function in multiple variables. This algorithm is based on a simple computationally verifiable necessity test for existence of a root in any compact set. Both theoretical analysis and numeric...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1999
ISSN: 0747-7171
DOI: 10.1006/jsco.1998.0272