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- Title
The Number of Complex Roots of a Univariate Polynomial Within a Rectangle.
- Authors
Cheng, C. C.; Lanel, G. H. J.
- Abstract
Let ƒ(z) be a nonzero complex univariate polynomial and let R be a rectangle in the complex plane. The number of complex roots of ƒ(z) inside R is given by the winding number of ƒ(z) on R if ƒ(z) has no roots on the boundary of R. In this paper the result is extended to all rectangles R even when ƒ(z) has roots on the boundary of R under the condition that ƒ(z) is square-free. It can also be used to formulate an algorithm that isolates the complex roots of any polynomial.
- Subjects
ROOTS of equations; COMPLEX numbers; MATHEMATICS; POLYNOMIALS; BOUNDARY value problems
- Publication
GSTF Journal of Mathematics, Statistics & Operations Research, 2014, Vol 2, Issue 1, p41
- ISSN
2251-3388
- Publication type
Article
- DOI
10.5176/2251-3388_2.2.50