Weight functions for Chebyshev quadrature
Author:
Yuan Xu
Journal:
Math. Comp. 53 (1989), 297302
MSC:
Primary 65D32
MathSciNet review:
970703
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Abstract: In this paper, we investigate if the weight function , where is a rational function of order (1,1), admits Chebyshev quadratures. Many positive examples are provided. In particular, we have proved that the answer is affirmative if , .
 [1]
Paul
F. Byrd and Lawrence
Stalla, Chebyshev quadrature rules for a new
class of weight functions, Math. Comp.
42 (1984), no. 165, 173–181. MR 725992
(85i:65030), http://dx.doi.org/10.1090/S00255718198407259921
 [2]
KlausJürgen
Förster, On weight functions admitting
Chebyshev quadrature, Math. Comp.
49 (1987), no. 179, 251–258. MR 890266
(89b:65061), http://dx.doi.org/10.1090/S00255718198708902668
 [3]
Walter
Gautschi, Advances in Chebyshev quadrature, Numerical analysis
(Proc. 6th Biennial Dundee Conf., Univ. Dundee, Dundee, 1975), Springer,
Berlin, 1976, pp. 100–121. Lecture Notes in Math., Vol. 506. MR 0468117
(57 #7956)
 [4]
Ja.
L. Geronimus, Čebyšev’s quadrature
formula, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969),
1182–1207 (Russian). MR 0259454
(41 #4092)
 [5]
Ja.
L. Geronīmus and A.
K. Medvedeva, The validity of the “ČebyŠev
rule” for a certain twoparameter family of weight functions,
Dokl. Akad. Nauk SSSR 224 (1975), no. 3,
516–518 (Russian). MR 0402365
(53 #6186)
 [6]
David
K. Kahaner, On equal and almost equal weight quadrature
formulas, SIAM J. Numer. Anal. 6 (1969),
551–556. MR 0286279
(44 #3492)
 [7]
Franz
Peherstorfer, Weight functions which admit Tchebycheff
quadrature, Bull. Austral. Math. Soc. 26 (1982),
no. 1, 29–37. MR 679918
(84k:65025), http://dx.doi.org/10.1017/S0004972700005578
 [8]
J.
L. Ullman, A class of weight functions that admit Tchebycheff
quadrature, Michigan Math. J. 13 (1966),
417–423. MR 0205463
(34 #5290)
 [1]
 P. F. Byrd & L. Stalla, "Chebyshev quadrature rules for a new class of weight functions," Math. Comp., v. 42, 1984, pp. 173181. MR 725992 (85i:65030)
 [2]
 K. J. Förster, "On weight functions admitting Chebyshev quadrature," Math Comp., v. 49, 1987, pp. 251258. MR 890266 (89b:65061)
 [3]
 W. Gautschi, Advances in Chebyshev Quadrature, Lecture Notes in Math., vol. 506, SpringerVerlag, Berlin and New York, 1976, pp. 100121. MR 0468117 (57:7956)
 [4]
 Ja. L. Geronimus, "On the Chebyshev quadrature formula," Izv. Akad. Nauk SSSR Ser. Mat., v. 33, 1969, pp. 11821207; English transl. in Math. USSRIzv., v. 3, 1969, pp. 11151138. MR 0259454 (41:4092)
 [5]
 Ja. L. Geronimus & A. K. Medvedeva, "The validity of the 'Chebyshev's rule' for a certain twoparameter family of weight functions," Dokl. Akad. Nauk SSSR, v. 224, 1975, pp. 516518; English transl. in Soviet Math. Dokl, v. 16, 1975, pp. 12311233. MR 0402365 (53:6186)
 [6]
 D. K. Kahaner, "On equal and almost equal weight quadrature formulas," SIAM J. Numer. Anal., v. 6, 1969, pp. 551556. MR 0286279 (44:3492)
 [7]
 F. Peherstorfer, "Weight functions which admit Tchebycheff quadrature," Bull. Austral. Math. Soc., v. 26, 1982, pp. 2938. MR 679918 (84k:65025)
 [8]
 J. L. Ullman, "A class of weight functions that admit Tchebycheff quadrature," Michigan Math. J., v. 13, 1966, pp. 417423. MR 0205463 (34:5290)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198909707032
PII:
S 00255718(1989)09707032
Keywords:
Chebyshev quadrature,
weight function with property T
Article copyright:
© Copyright 1989 American Mathematical Society
