A derivative-free algorithm for computing zeros of analytic functions
A derivative-free algorithm for computing zeros of analytic functions
Faculty of Social Sciences. Communication Sciences

article

1999
Wien
, 1999

Computer. Automation

Computing: archives for informatics and numerical computation. - Wien

63(1999)
:1
, p. 69-91

0010-485X

000081744400004

E

English (eng)

LetW be a simply connected region inC, f : W !Canalytic inW and a positively oriented Jordan curve in W that does not pass through any zero of f . We present an algorithm for computing all the zeros of f that lie in the interior of . It proceeds by evaluating certain integrals along numerically and is based on the theory of formal orthogonal polynomials. The algorithm requires only f and not its first derivative f 0. We have found that it gives accurate approximations for the zeros. Moreover, it is self-starting in the sense that it does not require initial approximations. The algorithmworks for simple zeros as well as multiple zeros, although it is unable to compute the multiplicity of a zero explicitly. Numerical examples illustrate the effectiveness of our approach.

https://repository.uantwerpen.be/docman/iruaauth/88dd31/045942e47b3.pdf

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