Computing zeros of analytic mappings : a logarithmic residue approachComputing zeros of analytic mappings : a logarithmic residue approach
Faculty of Social Sciences. Communication Sciences

Faculty of Political and Social Sciences - other

article

1998Lund, 1998

Computer. Automation

Bit : numerical mathematics. - Lund

38(1998):3, p. 583-596

0006-3835

000076573000010

E

English (eng)

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.

https://repository.uantwerpen.be/docman/iruaauth/6101ad/916a8035cbc.pdf

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