Rational Approximation and Interpolation
Volume 1105 of the series Lecture Notes in Mathematics pp 170181
Square blocks and equioscillation in the Padé, walsh, and cf tables
 Lloyd N. TrefethenAffiliated withCourant Institute of Mathematical Sciences, New York University
Abstract
It is well known that degeneracies in the form of repeated entries always occupy square blocks in the Padé table, and likewise in the Walsh table of real rational Chebyshev approximants on an interval. The same is true in complex CF (CarathéodoryFejér) approximation on a circle. We show that these block structure results have a common origin in the existence of equioscillationtype characterization theorems for each of these three approximation problems. Consideration of position within a block is then shown to be a fruitful guide to various questions whose answers are affected by degeneracy.
 Title
 Square blocks and equioscillation in the Padé, walsh, and cf tables
 Book Title
 Rational Approximation and Interpolation
 Book Subtitle
 Proceedings of the United Kingdom  United States Conference held at Tampa, Florida, December 12–16, 1983
 Pages
 pp 170181
 Copyright
 1984
 DOI
 10.1007/BFb0072410
 Print ISBN
 9783540138990
 Online ISBN
 9783540391135
 Series Title
 Lecture Notes in Mathematics
 Series Volume
 1105
 Series ISSN
 00758434
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Lloyd N. Trefethen ^{(1)}
 Author Affiliations

 1. Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY
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