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A note on a problem of Saff and Varga concerning the degree of complex rational approximation to real valued functions
Author(s):
S. W.
Ellacott
Journal:
Bull. Amer. Math. Soc.
6
(1982),
218-220.
MSC (1980):
Primary 30E10;
Secondary 41A20, 41A25, 41A50
MathSciNet review:
640950
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Additional information
References:
- [1979] C. Bennet, K. Rudnick and J. Vaaler, Best uniform approximation by linear fractional transformations, J. Approximation Theory, 25, 204-224. MR 531411
- [1981] S. Ellacott, On the Faber transform and efficient numerical rational approximation, Forschungsinstitut für Mathematik, ETH Zürich, SIAM J. Numer. Anal. (submitted) MR 714694
- [1980] D. Gaier, Vorlesungen über Approximation im Komplexen, Birkhäuser, Basel. MR 604011
- [1981] M. Gutknecht, Rational CF approximation on a disc, on a circle and on an interval, Seminar für Angewandte Mathematik, ETH Zürich (in preparation).
- [1964] Ch. Pommerenke, Ueber die Faberschen Polynome Schlichter Funktionen, Math. Z. 85, 197-208. MR 168772
- [1967] Ch. Pommerenke, Konforme Abbildung und Fekete-Punkte, Math. Z. 89, 422-438. MR 181740
- [1977] A. Ruttan, On the cardinality of a set of best complex rational approximations to a real function, Padé and Rational Approximation (E. B. Saff and R. S. Varga, eds.), Academic Press, New York, pp. 303-319. MR 473647
- [1977] E. B. Saff and R. S. Varga, Nonuniqueness of best approximating complex rational functions, Bull. Amer. Math. Soc. 83, 375-377. MR 433108
- [1978] E. B. Saff and R. S. Varga Nonuniqueness of best complex rational approximations to real functions on real intervals, J. Approximation Theory, 23, 78-85. MR 499031
- [1981a] L. Trefethen, Near circularity of the error curve in complex Chebyshev approximation, J. Approximation Theory, 31, 344-366. MR 628517
- [1981b] L. Trefethen, Rational Chebyshev approximation on the unit disc, Numer. Math. 37, 297-320. MR 623046
- [1979] L. Trefethen, Near circularity of the error curve in complex Chebyshev approximation, Computer Science Dept., Stanford Univ., J. Approximation Theory (to appear).
- [1980] L. Trefethen, Rational Chebyshev approximation on the unit disc, Stanford NAP manuscript NA-80-08, Stanford Univ., California, Numer. Math, (submitted). MR 623046
- [1978] D. Wulbert, The rational approximation of real functions, Amer. J. Math. vol. 100, 1281-1315. MR 522701
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30E10, 41A20, 41A25, 41A50
Additional Information:
DOI:
10.1090/S0273-0979-1982-14987-4
PII:
S 0273-0979(1982)14987-4
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