Title




Computing zeros of analytic mappings : a logarithmic residue approach


Author






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. 


Language




English


Source (journal)




Bit : numerical mathematics.  Lund
Bit : numerical mathematics.  Lund


Publication




Lund
:
1998


ISSN




00063835
[print]
15729125
[online]


Volume/pages




38
:3
(1998)
, p. 583596


ISI




000076573000010


Full text (Publisher's DOI)






Full text (publisher's version  intranet only)





