Title Computing zeros of analytic mappings : a logarithmic residue approach Author Kravanja, Peter Cools, Ronald Haegemans, Ann Faculty/Department Faculty of Social Sciences. Communication Sciences Publication type article Publication 1998 Lund , 1998 Subject Computer. Automation Source (journal) Bit : numerical mathematics. - Lund Volume/pages 38(1998) :3 , p. 583-596 ISSN 0006-3835 ISI 000076573000010 Carrier E Target language English (eng) Full text (Publishers DOI) Abstract Let D be a polydisk in C ~ and f : D --+ C n a mapping that is analytic in D and has no zeros on the boundary of D. Then f has only a finite number of zeros in D and these zeros are all isolated. We consider the problem of computing these zeros. A multidimensional generalization of the classical logarithmic residue formula from the theory of functions of one complex variable will be our means of obtaining information about the location of these zeros. This integral formula involves the integral of a differential form, which we will transform into a sum of n Riemann integrals of dimension 2n - 1. We will show how the zeros and their multiplicities can be computed from these integrals by solving a generalized eigenvalue problem that has Hankel structure, and n Vandermonde systems. Numerical examples are included. E-info https://repository.uantwerpen.be/docman/iruaauth/6101ad/916a8035cbc.pdf http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000076573000010&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000076573000010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000076573000010&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848