Title 



A derivativefree 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 selfstarting 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 



0010485X


Volume/pages 



63:1(1999), p. 6991


ISI 



000081744400004


Full text (Publishers DOI) 


 

Full text (publishers version  intranet only) 


 
