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Best uniform rational approximation of $x^\alpha $ on $[0,1]$
Author(s):
Herbert
Stahl
Journal:
Bull. Amer. Math. Soc.
28
(1993),
116-122.
MSC (1991):
Primary 41A20, 41A25, 41A50
MathSciNet review:
1168517
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References:
- [Be1]
- S. Bernstein, Sur meilleure approximation de $|x|$ par des polyn\^omes de degr\'es donn\'es, Acta Math. \textbf{37} (1913), 1--57. MR
- [Be2]
- S. Bernstein, About the best approximation of $|x|^p$ by means of polynomials of very high degree, Bull. Acad. Sci. USSR Cl. Sci. Math. Natur. 2 (1938), 169--190. MR
- [Bu1]
- A. P. Bulanow, Asymptotics for the least derivation of $|x|$ from rational functions, Mat. Sb. \textbf{76} (1968), 288--303. MR 228889
- [Bu2]
- A. P. Bulanow, The approximation of $x^{1/3}$ by rational functions, Vests\B \i Akad. Navuk BSSR Ser. F\B \i z.-Mat. Navuk \textbf{2} (1968), 47--56 \afterall (Russian). MR 231094
- [FrSz]
- G. Freud and J. Szabados, Rational approximation to $x^\alpha $, Acta Math. Acad. Sci. Hungar. \textbf{18} (1967), 393--399. MR 221169
- [Ga]
- T. Ganelius, Rational approximation to $x^\alpha $ on $[0,1]$, Anal. Math. \textbf{5} (1979), 19--33. MR 535494
- [GoLa]
- A. H. Gonchar and G. Lopez, On Markov's theorem for multipoint Pade\'e approximants, Mat. Sb. \textbf{105} (1978). MR
- [Go1]
- A. A. Gonchar, On the speed of rational approximation of continuous functions with characteristic singularities, Mat. Sb. \textbf{73} (1967), 630--638. MR 214982
- [Go2]
- A. A. Gonchar, Rational approximation of the function $x^\alpha $, Constructive Theory of Functions (Proc. Internat. Conf., Varna 1970), Izdat. Bolgar. Akad. Nauk, Sofia, 1972, pp.~51--53 \afterall (Russian). MR 364959
- [Go3]
- A. A. Gonchar, The rate of rational approximation and the property of single-valuedness of an analytic function in a neighborhood of an isolated singular point, Mat. Sb. \textbf{94} (1974), 265--282. MR 352477
- [Me]
- G. Meinardus, Approximation of functions\,{\rm :} Theory and numerical methods, Springer-Verlag, New York, 1967. MR 217482
- [Ne]
- D. J. Newman, Rational approximation to $|x|$, Michigan Math. J. \textbf{11} (1964), 11--14. MR 171113
- [Ri]
- T. J. Rivlin, An introduction to the approximation of functions, Blaisdell Publ. Co., Waltham, MA, 1969. MR 634509
- [St]
- H. Stahl, Best uniform rational approximation of $|x|$ on $[-1,1]$, Mat. Sb. {\bf 183} (1992), no. 8, 85--118; English transl. in Russian Acad. Sci. Sb. Math. {\bf 76} (1993), no. 2 (to appear). MR 1187250
- [StTo]
- H. Stahl and V. Totik, General orthogonal polynomials, Cambridge Univ. Press, New York, 1992. MR 1163828
- [Tz]
- J. Tzimbalario, Rational approximation to $x^\alpha $, J. Approx. Theory \textbf{16} (1976), 187--193. MR 402344
- [VC1]
- R. S. Varga and A. J. Carpenter, On the Bernstein Conjecture in approximation theory, Constr. Approx. \textbf{1} (1985), 333--348. MR 891763
- [VC2]
- R. S. Varga and A. J. Carpenter, Some numerical results on best uniform rational approximation of $x^\alpha $ on $[0,1]$, Numer. Algorithms. MR 1165904
- [VCR]
- R. S. Varga, A. Ruttan, and A. J. Carpenter, Numerical results on best uniform rational approximation of $|x|$ on $[-1,1]$, Mat. Sb. \textbf{182} (1991), 1523--1541; English transl. in Math. USSR Sb. {\bf 74} (1993), no. 2 (to appear). MR 1137861
- [Vj1]
- N. S. Vjacheslavov, The approximation of $|x|$ by rational functions, Mat. Zametki \textbf{16} (1974), 163--171; English transl. in Math. Notes {\bf 16} (1974), 680--685. MR 355426
- [Vj2]
- N. S. Vjacheslavov, On the uniform approximation of $|x|$ by rational functions, Dokl. Akad. Nauk SSSR \textbf{220} (1975), 512--515. MR 380214
- [Vj3]
- N. S. Vjacheslavov, On the approximation of $x^\alpha $ by rational functions, Izv. Akad. Nauk USSR \textbf{44} (1980). MR 563787
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Additional Information:
DOI:
10.1090/S0273-0979-1993-00351-3
PII:
S 0273-0979(1993)00351-3
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