Title
Computing zeros of analytic mappings : a logarithmic residue approach
Author
Faculty/Department
Faculty of Social Sciences. Communication Sciences
Publication type
article
Publication
Lund ,
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
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