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| Content Provider | Springer Nature Link |
|---|---|
| Author | Baratchart, Laurent Yattselev, Maxim |
| Copyright Year | 2009 |
| Abstract | We consider multipoint Padé approximation to Cauchy transforms of complex measures. We show that if the support of a measure is an analytic Jordan arc and if the measure itself is absolutely continuous with respect to the equilibrium distribution of that arc with Dini-smooth nonvanishing density, then the diagonal multipoint Padé approximants associated with appropriate interpolation schemes converge locally uniformly to the approximated Cauchy transform in the complement of the arc. This asymptotic behavior of Padé approximants is deduced from the analysis of underlying non-Hermitian orthogonal polynomials, for which we use classical properties of Hankel and Toeplitz operators on smooth curves. A construction of the appropriate interpolation schemes is explicit granted the parametrization of the arc. |
| Ending Page | 715 |
| Page Count | 41 |
| Starting Page | 675 |
| File Format | |
| ISSN | 16153375 |
| e-ISSN | 16153383 |
| Journal | Foundations of Computational Mathematics |
| Issue Number | 6 |
| Volume Number | 9 |
| Language | English |
| Publisher | Springer-Verlag |
| Publisher Date | 2009-03-17 |
| Publisher Place | New York |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Economics general Orthogonal functions and polynomials, general theory Linear and Multilinear Algebras, Matrix Theory Orthogonal polynomials with varying weights Non-Hermitian orthogonality Approximation by rational functions Strong asymptotics Numerical Analysis Multipoint Padé approximation Computer Science Math Applications in Computer Science Applications of Mathematics Padé approximation |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Analysis Computational Theory and Mathematics Computational Mathematics |
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