Helton, J. W., Spain, P. G. and Young, N. J. (1990) Tracking poles and representing Hankel operators directly from data. Numerische Mathematik, 58(1), pp. 641-660. (doi: 10.1007/BF01385646)
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Abstract
We propose and analyse a method of estimating the poles near the unit circleT of a functionG whose values are given at a grid of points onT: we give an algorithm for performing this estimation and prove a convergence theorem. The method is to identify the phase for an estimate by considering the peaks of the absolute value ofG onT, and then to estimate the modulus by seeking a bestL 2 fit toG over a small arc by a first order rational function. These pole estimates lead to the construction of a basis ofL 2 which is well suited to the numerical representation of the Hankel operator with symbolG and thereby to the numerical solution of the Nehari problem (computing the bestH ∞, analytic, approximation toG relative to theL ∞ norm), as analysed in [HY]. We present the results of numerical tests of these algorithms.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Spain, Dr Philip |
Authors: | Helton, J. W., Spain, P. G., and Young, N. J. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Numerische Mathematik |
Publisher: | Springer-Verlag |
ISSN: | 0029-599X |
ISSN (Online): | 0945-3245 |
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