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