Bibliography for Chebyshev Quadrature

unabridged

 

  1. Convergence Acceleration of Gauss-Chebyshev Quadrature Formulae
    Kzaz, M.; Prevost, M.
    Numerical Algorithms, 2003, vol. 34, no. 2/4, pp. 379-391, Ingenta.  
  2. New quadrature formulas based on the zeros of the chebyshev polynomials of the second kind
    Yang, S.; Wang, X.
    Computers and Mathematics With Applications, 2003, vol. 45, no. 10/11, pp. 1611-1618, Ingenta.  
  3. Chebyshev-Markov-Bernstein-Szego Polynomials and Quadrature Formulas with Enhanced Precision for Some Classes of Integrals with Parameter-Dependent Weight Functions
    Lebedev, V. I.
    Doklady Mathematics, 2003, vol. 67, no. 3, pp. 398-403, Ingenta.  
  4. Fourier-Chebyshev Coefficients and Gauss-Turan Quadrature with Chebyshev Weight
    Yang, S.; Wang, X.
    Journal of Computational Mathematics, 2003, vol. 21, no. 2, pp. 189-194, Ingenta.  
  5. H2-optimal quadrature formula with Chebyshev weight of the second kind. Justification of the nodes asymptotics
    Samokish, B. A.
    St Petersburg Mathematical Journal, 2002, vol. 13, no. 5, pp. 827-858, Ingenta.  
  6. Quadrature formulas for Fourier-Chebyshev coefficients
    Yang, S.-j.
    Journal- Zhejiang University Science, 2002, vol. 3, no. 3, pp. 326-331, Ingenta.  
  7. Presentation of Legendre Polynomials Through Chebyshev Polynomials: A Method for Calculation of Nodes and Weights of Gauss Quadrature, Numerical Integration of Functions near Power Singularities
    Rempel, H. H.
    Doklady Earth Sciences, 2002, vol. 383, no. 2, pp. 154-156, Ingenta.
  8. A Chebyshev quadrature rule for one sided finite part integrals.  
    Kim, Philsu
    J. Approx. Theory  111  (2001),  no. 2, 196--219, MathSciNet.  
  9. Interpolatory quadrature formulae with Chebyshev abscissae.    
    Notaris, Sotirios E.    
    Journal of Computational and Applied Mathematics, 133 (2001), no. 1-2, 507--517, MathSciNet.  
  10. Generalized Gaussian Quadrature Formulas with Chebyshev Nodes.
    Shi, Ying-guang
    Journal of computational mathematics, 1999, vol. 17, no. 2, pp. 171-178, Ingenta.  
  11. On Gaussian quadrature formulas for the Chebyshev weight.    
    Shi, Ying Guang    
    J. Approx. Theory 98 (1999), no. 1, 183--195, MathSciNet.  
  12. On Turán Quadrature Formulas for the Chebyshev Weight.
    Shi, Ying Guang
    Journal of approximation theory, 1999, vol. 96, no. 1, pp. 101-110, Ingenta.  
  13. Gauss-Chebyshev quadrature formulae for strongly singular integrals
    Korsunsky, Alexander M.  
    Quarterly of Applied Mathematics, v 56, n 3, Sep, 1998, p 461-472, Compendex.
  14. Gaussian quadrature of Chebyshev polynomials.    
    Hunter, D. B.; Nikolov, Geno    
    J. Comput. Appl. Math. 94 (1998), no. 2, 123--131, MathSciNet.  
  15. New interpolatory quadrature formulae with Chebyshev abscissae
    Notaris, Sotirios E.  
    Journal of Computational and Applied Mathematics, v 94, n 2, Aug 3, 1998, p 199-214, Compendex.
  16. General Gaussian quadrature formulas on Chebyshev nodes.    
    Shi, Yingguang    
    Adv. Math. (China) 27 (1998), no. 3, 227--239, MathSciNet.  
  17. A note on Gaussian type quadrature formulas with Chebyshev weight functions. (Chinese)    
    Lu, Wan Jin; Xiao, Xiang Wu; Zhang, Fa Yong    
    Heilongjiang Daxue Ziran Kexue Xuebao 15 (1998), no. 3, 1--2, 6, MathSciNet.  
  18. Interpolatory quadrature formulae with Chebyshev abscissae of the third or fourth kind.
    Notaris, S.E.
    Journal of computational and applied mathematics, 1997, vol. 81, no. 1, pp. 83, Ingenta.  
  19. Chebyshev-Type Quadrature and Partial Sums of the Exponential Series  
    Arno Kuijlaars
    Mathematics of Computation, Vol. 64, No. 209. (Jan., 1995), pp. 251-263, Jstor.  
  20. Chebyshev-type quadrature for Jacobi weight functions.
    Kuijlaars, A.
    Journal of computational and applied mathematics, 1995, vol. 57, no. 1/2, pp. 171, Ingenta.  
  21. Chebyshev quadrature for measures with a strong singularity.
    Kuijlaars, A. B. J.
    Journal of Computational and Applied Mathematics. 65 (1995), no. 1-3, 207--214, MathSciNet.  
  22. Chebyshev-type quadrature and zeros of Faber polynomials
    Kuijlaars, A.B.J.
    Journal of Computational and Applied Mathematics, v 62, n 2, Sep 20, 1995, p 155, Compendex.
  23. On a Theorem of C. Posse Concerning Gaussian Quadrature of Chebyshev Type  
    Klaus-Jurgen Forster
    Mathematics of Computation, Vol. 62, No. 206. (Apr., 1994), pp. 719-724, Jstor.  
  24. Accurate and efficient numerical integration of weight functions using Gauss-Chebyshev quadrature
    Daniewicz, Steven R.  
    Engineering Fracture Mechanics, v 48, n 4, Jul, 1994, p 541-544, Compendex.
  25. A note on quadrature formulas for the Chebyshev weight function of the first kind.    
    Pérez-Acosta, F.; González-Vera, P.    
    Appl. Math. Lett. 7 (1994), no. 3, 97--100, MathSciNet.  
  26. Chebyshev-Type Quadrature on Multidimensional Domains.
    Meyers, J.L.H.; Korevaar, J.
    Journal of approximation theory, 1994, vol. 79, no. 1, pp. 144, Ingenta.  
  27. A Chebyshev-type quadrature rule with some interesting properties (Letter).
    Shi Ranga, A.; Velga, M.
    Journal of Computational and Applied Mathematics, v 51, n 2, June 20, 1994, p 263, Compendex.
  28. The minimal number of nodes in Chebyshev type quadrature formulas.
    Kuijlaars, Arno
    Indagationes mathematicae, 1993, vol. 4, no. 3, pp. 339, Ingenta.  
  29. On Gauss-Kronrod Quadrature Formulae of Chebyshev Type  
    Sotirios E. Notaris  
    Mathematics of Computation, Vol. 58, No. 198. (Apr., 1992), pp. 745-753, Jstor.  
  30. Bounds for the Number of Nodes in Chebyshev Type Quadrature Formulas.
    Rabau, Patrick; Bajnok, Bela
    Journal of approximation theory, 1991, vol. 67, no. 2, pp. 199, Ingenta.  
  31. A Note on the Contour Integral Representation of the Remainder Term for a Gauss-Chebyshev Quadrature Rule  
    Walter Gautschi; E. Tychopoulos; R. S. Varga  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 1. (Feb., 1990), pp. 219-224, Jstor.  
  32. Weight Functions for Chebyshev Quadrature  
    Yuan Xu  
    Mathematics of Computation, Vol. 53, No. 187. (Jul., 1989), pp. 297-302, Jstor.  
  33. Numerical integration with linear combination of Chebyshev-Gauss quadratures.    
    Hajósy, A.    
    Ann. Univ. Sci. Budapest. Sect. Comput. 9 (1989), 139--149, MathSciNet.  
  34. Automatic Quadrature On Chebyshev Points.
    Geppini, M.; Romani, F.
    Computers & Mathematics with Applications, v 16, n 3, 1988, p 185-193, Compendex.
  35. On Chebyshev quadrature and variance of quadrature formulas.
    Förster, Klaus-Jürgen
    BIT 28 (1988), no. 2, 360--363, MathSciNet.  
  36. Construction of Chebyshev quadrature formulas for path integrals of a certain type. (Russian)
    Marnevskaya, L. A.; Yanovich, L. A.
    Dokl. Akad. Nauk BSSR 32 (1988), no. 7, 591--594, 668--669, MathSciNet.  
  37. On Weight Functions Admitting Chebyshev Quadrature  
    Klaus-Jurgen Forster  
    Mathematics of Computation, Vol. 49, No. 179. (Jul., 1987), pp. 251-258, Jstor.  
  38. Exponentially convergent Fourier-Chebyshev quadrature schemes on bounded and infinite intervals.
    Boyd, John P.
    J. Sci. Comput. 2 (1987), no. 2, 99--109, MathSciNet.  
  39. On Chebyshev quadrature for ultraspherical weight functions.
    Förster, K.-J.
    Calcolo 23 (1986), no. 4, 355--381 (1987), MathSciNet.  
  40. On Weighted Chebyshev-Type Quadrature Formulas  
    Klaus-Jurgen Forster, Georg-Peter Ostermeyer  
    Mathematics of Computation, Vol. 46, No. 174. (Apr., 1986), pp. 591-599, Jstor.  
  41. Supplement to On Weighted Chebyshev-Type Quadrature Formulas  
    Klaus-Jurgen Forster, Georg-Peter Ostermeyer  
    Mathematics of Computation, Vol. 46, No. 174. (Apr., 1986), pp. S21-S27, Jstor.  
  42. Corrigendum: "Generalized Chebyshev interpolation and its application to automatic quadrature"
    Hasegawa, Takemitsu
    Math. Comp. 47 (1986), no. 175, 385, MathSciNet.
  43. On Chebyshev Quadrature For A Special Class Of Weight Functions.
    Foerster, Klaus-Juergen  
    BIT (Copenhagen), v 26, n 3, 1986, p 327-332, Compendex.
  44. Numerical integration of functions by means of Chebyshev-type interpolation polynomials. (Russian)    
    Klokov, Yu. A.; Shkerstena, A. Ya.    
    Latv. Mat. Ezhegodnik No. 30 (1986), 207--217, 263, MathSciNet.  
  45. Multivariable integration based on generalized Chebyshev interpolation. (Japanese)    
    Hasegawa, Takemitsu; Torii, Tatsuo
    Algorithms for parallel numerical calculation (Japanese) (Kyoto, 1985).
    Surikaisekikenkyusho Kokyuroku No. 585 (1986), 207--222, MathSciNet.
  46. A Chebyshev-type quadrature for eighteen nodes.    
    Matsuda, Takashi; Yanagiwara, Hiroki    
    Bull. Fukuoka Univ. Ed. III 35 (1985), 47--49 (1986), MathSciNet.  
  47. Chebyshev Quadrature Rules for a New Class of Weight Functions  
    Paul F. Byrd, Lawrence Stalla  
    Mathematics of Computation, Vol. 42, No. 165. (Jan., 1984), pp. 173-181, Jstor.  
  48. Generalized Chebyshev Interpolation and Its Application to Automatic Quadrature  
    Takemitsu Hasegawa, Tatsuo Torii, Ichizo Ninomiya  
    Mathematics of Computation, Vol. 41, No. 164. (Oct., 1983), pp. 537-553, Jstor.  
  49. Numerical solution of singular integral equations using Gauss-type formulae. II. Lobatto-Chebyshev quadrature and collocation on Chebyshev nodes.
    Srivastav, R. P.; Jen, Erica
    IMA J. Numer. Anal. 3 (1983), no. 3, 319--325, MathSciNet.  
  50. Chebyshev's quadrature formulas for a class of Wiener double integrals. (Russian)
    Yanovich, L. A.
    Dokl. Akad. Nauk BSSR 27 (1983), no. 4, 293--296, MathSciNet.  
  51. On the existence of approximate solutions for singular integral equations of Cauchy type discretized by Gauss-Chebyshev quadrature formulae.
    Gerasoulis, Apostolos
    BIT 21 (1981), no. 3, 377--380, MathSciNet.  
  52. On characterization of functions by their Gauss-Chebyshev quadratures.
    Borosh, Itshak; Chui, Charles K.
    SIAM J. Math. Anal. 10 (1979), no. 3, 532--541, MathSciNet.  
  53. Almost-interpolatory Chebyshev quadrature. II.
    Salkauskas, K.
    Proceedings of the Sixth Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1976), pp. 381--388, Congress. Numer., XVIII, Utilitas Math., Winnipeg, Man., 1977, MathSciNet.  
  54. Advances in Chebyshev quadrature.  
    Gautschi, Walter
    Numerical analysis (Proc. 6th Biennial Dundee Conf., Univ. Dundee, Dundee, 1975),  pp. 100--121. Lecture Notes in Math., Vol. 506, Springer, Berlin, 1976, MathSciNet.  
  55. Nonexistence of Chebyshev-Type Quadratures on Infinite Intervals  
    Walter Gautschi  
    Mathematics of Computation, Vol. 29, No. 129. (Jan., 1975), pp. 93-99, Jstor.  
  56. Gauss-Turan Quadratures Of Chebyshev Type And Error Formulae.
    Riess, R. D.
    Computing (Vienna/New York), v 15, n 3, 1975, p 173-179, Compendex.  
  57. On weight functions for Chebyshev quadrature.
    Salkauskas, K.
    Numer. Math. 24 (1975), 13--18, MathSciNet.  
  58. On Chebyshev-Type Quadratures  
    Walter Gautschi; Hiroki Yanagiwara  
    Mathematics of Computation, Vol. 28, No. 125. (Jan., 1974), pp. 125-134, Jstor.  
  59. Almost-Interpolatory Chebyshev Quadrature  
    K. Salkauskas  
    Mathematics of Computation, Vol. 27, No. 123. (Jul., 1973), pp. 645-654, Jstor.  
  60. A Chebyshev quadrature formula for twelve nodes.
    Yanagiwara, Hiroki; Shibata, Kiyomi
    Bull. Fukuoka Univ. Ed. III 23 (1973), 45--51, MathSciNet.  
  61. Error bounds for a Chebyshev quadrature scheme.
    Kambo, N. S.
    Nordisk Tidskr. Informationsbehandling (BIT) 13 (1973), 30--37, MathSciNet.  
  62. Concerning Gaussian-Chebyshev Quadrature Errors  
    Charles K. Chui  
    SIAM Journal on Numerical Analysis, Vol. 9, No. 2. (Jun., 1972), pp. 237-240, Jstor.  
  63. On the Gaussian Integration of Chebyshev Polynomials  
    A. R. Curtis, P. Rabinowitz  
    Mathematics of Computation, Vol. 26, No. 117. (Jan., 1972), pp. 207-211, Jstor.  
  64. A Note on Error Bounds for Gauss-Chebyshev Quadrature  
    R. D. Riess  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 3. (Sep., 1971), pp. 509-511, Jstor.  
  65. On the Error in the Numerical Integration of Chebyshev Polynomials  
    D. Nicholson, P. Rabinowitz, N. Richter, D. Zeilberger  
    Mathematics of Computation, Vol. 25, No. 113. (Jan., 1971), pp. 79-86, Jstor.  
  66. Best Chebyshev quadratures.
    Franke, Richard
    Rocky Mountain J. Math. 1 1971 no. 3, 499--508, MathSciNet.  
  67. Error Estimates for a Chebyshev Quadrature Method  
    N. K. Basu  
    Mathematics of Computation, Vol. 24, No. 112. (Oct., 1970), pp. 863-867, Jstor.  
  68. Chebyshev Type Quadrature Formulas  
    David K. Kahaner  
    Mathematics of Computation, Vol. 24, No. 111. (Jul., 1970), pp. 571-574, Jstor.  
  69. Chebyshev-Type Integration Rules of Minimum Norm  
    Philip Rabinowitz, Nira Richter  
    Mathematics of Computation, Vol. 24, No. 112. (Oct., 1970), pp. 831-845, Jstor.  
  70. Error Bounds for Some Chebyshev Methods of Approximation and Integration  
    Christopher T. H. Baker, Pauline A. Radcliffe  
    SIAM Journal on Numerical Analysis, Vol. 7, No. 2. (Jun., 1970), pp. 317-327, Jstor.  
  71. Estimation of errors of Gauss-Chebyshev quadratures.
    Chawla, M. M.
    Comput. J. 13 1970 107--109, MathSciNet.  
  72. Estimating Gauss-Chebyshev Quadrature Errors  
    R. D. Riess, L. W. Johnson  
    SIAM Journal on Numerical Analysis, Vol. 6, No. 4. (Dec., 1969), pp. 557-559, Jstor.  
  73. New Type of Chebyshev Quadrature (in Technical Notes and Short Papers)  
    R. E. Barnhill, J. E. Dennis, Jr., G. M. Nielson  
    Mathematics of Computation, Vol. 23, No. 106. (Apr., 1969), pp. 437-441, Jstor.  
  74. Chebyshev interpolation and quadrature formulas of very high degree.   
    Salzer, Herbert E.   
    Comm. ACM 12 (1969), 271; errata, ibid. 12 1969 385, MathSciNet.
  75. On Davis's method for the estimation of errors of Gauss-Chebyshev quadratures.
    Chawla, M. M.
    SIAM J. Numer. Anal. 6 1969 108--117, MathSciNet.  
  76. Construction of Chebyshev Quadrature Formulae (in Classroom Notes)  
    K. Salkauskas  
    American Mathematical Monthly, Vol. 75, No. 10. (Dec., 1968), pp. 1099-1101, Jstor.  
  77. Error Bounds for the Gauss-Chebyshev Quadrature Formula of the Closed Type (in Technical Notes and Short Papers)  
    M. M. Chawla  
    Mathematics of Computation, Vol. 22, No. 104. (Oct., 1968), pp. 889-891, Jstor.  
  78. Error Bounds for Gauss-Chebyshev Quadrature (in Technical Notes and Short Papers)  
    Franz Stetter  
    Mathematics of Computation, Vol. 22, No. 103. (Jul., 1968), pp. 657-659, Jstor.  
  79. The Non-Existence of Certain Laguerre-Chebyshev Quadrature Formulas
    F. D. Burgoyne
    Mathematics of Computation, Vol. 17, No. 82. (Apr., 1963), pp. 196-197, Jstor.  
  80. Tables for facilitating the use of Chebyshev's quadrature formula.
    Salzer, Herbert E.
    J. Math. Phys. Mass. Inst. Tech. 26, (1947). 191--194, MathSciNet.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004