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Title
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A derivative-free algorithm for computing zeros of analytic functions
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Author
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Abstract
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| 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. |
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Language
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English
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Source (journal)
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Computing: archives for informatics and numerical computation. - Wien
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Publication
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Wien
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1999
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ISSN
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0010-485X
[print]
1436-5057
[online]
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DOI
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10.1007/S006070050051
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Volume/pages
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63
:1
(1999)
, p. 69-91
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ISI
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000081744400004
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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