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Complex root isolation. Jayantha Lanel Gan Hewage

Complex root isolation.

Jayantha Lanel Gan Hewage

Published
ISBN : 9781109278217
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45 pages
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 About the Book 

Let A(z) be a univariate polynomial with positive degree. Isolating all the distinct roots of A into disjoint isolating rectangles is called complex root isolation. The complex root isolation of A(z) can be done by reducing the problem to finding anMoreLet A(z) be a univariate polynomial with positive degree. Isolating all the distinct roots of A into disjoint isolating rectangles is called complex root isolation. The complex root isolation of A(z) can be done by reducing the problem to finding an algorithm to determine the number of roots of A(z) in any given closed rectangle R in the complex plane. If there is no zeros of A(z) on the boundary of R, then the number of roots in R can be obtained by using the argument principle. However, it fails when the last hypothesis does not hold. In this thesis a solution is given even if the hypothesis is dropped.-The algorithm is implemented in SacLib 2.1 (a library of C functions for symbolic computation) to show that it is efficient in practice.