Real and complex Chebyshev approximation on the unit disk and interval

Authors:
Martin H. Gutknecht and Lloyd N. Trefethen

Journal:
Bull. Amer. Math. Soc. **8** (1983), 455-458

MSC (1980):
Primary 30E10; Secondary 41A20

DOI:
https://doi.org/10.1090/S0273-0979-1983-15118-2

MathSciNet review:
693961

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References | Similar Articles | Additional Information

**1.**C. K. Chui, O. Shisha and P. W. Smith,*Padé approximants as limits of best rational approximants*, J. Approx. Theory 12 (1974), 201-204. MR**358160****2.**S. W. Ellacott,*A note on a problem of Saff and Varga concerning the degree of complex rational approximation to real valued functions*, Bull. Amer. Math. Soc. (N.S.)**6**(1982), no. 2, 218–220. MR**640950**, https://doi.org/10.1090/S0273-0979-1982-14987-4**3.**Martin H. Gutknecht and Lloyd N. Trefethen,*Nonuniqueness of best rational Chebyshev approximations on the unit disk*, J. Approx. Theory**39**(1983), no. 3, 275–288. MR**720942**, https://doi.org/10.1016/0021-9045(83)90099-0**4.**K. N. Lungu,*Best approximation by rational functions*, Mat. Z. 10 (1971), 11-15. (Russian) MR**290004****5.**A. Ruttan,*On the cardinality of a set of best complex rational approximations to real function*, Padé and Rational Approximation (E. B. Saff and R. S. Varga, eds.), Academic Press, New York, 1977, pp. 303-319. MR**473647****6.**E. B. Saff and R. S. Varga,*Nonuniqueness of best approximating complex rational functions*, Bull. Amer. Math. Soc. 83 (1977), 375-377. MR**433108****7.**E. B. Saff and R. S. Varga,*Nonuniqueness of best complex rational approximations to real functions on real intervals*, J. Approx. Theory**23**(1978), no. 1, 78–85. MR**499031**, https://doi.org/10.1016/0021-9045(78)90081-3**8.**Lloyd N. Trefethen and Martin H. Gutknecht,*Real vs. complex rational Chebyshev approximation on an interval*, Trans. Amer. Math. Soc.**280**(1983), no. 2, 555–561. MR**716837**, https://doi.org/10.1090/S0002-9947-1983-0716837-X**9.**Richard S. Varga,*Topics in polynomial and rational interpolation and approximation*, Séminaire de Mathématiques Supérieures [Seminar on Higher Mathematics], vol. 81, Presses de l’Université de Montréal, Montreal, Que., 1982. MR**654329****10.**J. L. Walsh,*Interpolation and approximation by rational functions in the complex domain*, 5th. ed., Amer. Math. Soc. Colloq. Publ., vol. 20, Amer. Math. Soc. Providence, R.I., 1966. MR**218588****11.**J. L. Walsh,*Padé approximants as limits of rational functions of best approximation*, J. Math. Mech. 13 (1964), 305-312. MR**161074****12.**J. L. Walsh,*Padé approximants as limits of rational functions of best approximation, real domain*, J. Approx. Theory 11 (1974), 225-230. MR**352801**

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DOI:
https://doi.org/10.1090/S0273-0979-1983-15118-2