Publication: Determining system poles using row sequences of orthogonal Hermite–Padé approximants
Issued Date
2018-07-01
Resource Type
ISSN
10960430
00219045
00219045
Other identifier(s)
2-s2.0-85046786574
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Mahidol University
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SCOPUS
Bibliographic Citation
Journal of Approximation Theory. Vol.231, (2018), 15-40
Suggested Citation
N. Bosuwan, G. López Lagomasino Determining system poles using row sequences of orthogonal Hermite–Padé approximants. Journal of Approximation Theory. Vol.231, (2018), 15-40. doi:10.1016/j.jat.2018.04.005 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/46103
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Title
Determining system poles using row sequences of orthogonal Hermite–Padé approximants
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Abstract
© 2018 Elsevier Inc. Given a system of functions F=(F1,…,Fd), analytic on a neighborhood of some compact subset E of the complex plane with simply connected complement in the extended complex plane, we define a sequence of vector rational functions with common denominator in terms of the orthogonal expansions of the components Fi,i=1,…,d, with respect to a sequence of orthonormal polynomials associated with a measure μ whose support is contained in E. Such sequences of vector rational functions resemble row sequences of type II Hermite–Padé approximants. Under appropriate assumptions on μ, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of the sequence of vector rational functions so constructed. The exact rate of convergence of these denominators is provided and the rate of convergence of the simultaneous approximants is estimated. It is shown that the common denominators of the approximants detect the location of the poles of the system of functions.