Bibliography for the Rational Approximation

short

 

  1. Constrained interpolation with rational cubics
    Meek, D. S.; Ong, B. H.; Walton, D. J.
    Computer Aided Geometric Design, 2003, vol. 20, no. 5, pp. 253-275, Intenta.  
  2. G2 Two-Point Hermite Rational Cubic Interpolation
    Habib, Z.; Sakai, M.
    International Journal of Computer Mathematics, 2002, vol. 79, no. 11, pp. 1225-1232, Intenta.  
  3. Rational approximations to power expansions  
    Aguilera-Navarro, Maria Cecília K.; Aguilera-Navarro, Valdir C.; Ferreira, Ricardo C.; Teramon, Neuza
    College Math. J. 32 (2001), no. 4, 276--278.
  4. Hybrid Rational Function Approximation and Its Accuracy Analysis
    Kai, H.; Noda, M.-T.
    Reliable Computing, 2000, vol. 6, no. 4, pp. 429-438, Intenta.   
  5. Simultaneous stabilization of linear systems and interpolation with rational functions.
    Blondel, Vincent D.
    Open problems in mathematical systems and control theory, 53--59, Comm. Control Engrg. Ser., Springer, London, 1999, MathSciNet.  
  6. A note on rational approximations.
    Adiga, Chandrashekar; Vasuki, K. R.
    J. Indian Math. Soc. (N.S.) 65 (1998), no. 1-4, 181--189.
  7. Low degree rational spline interpolation.
    Oja, P.
    BIT, 1997, vol. 37, no. 4, pp. 901, Intenta.   
  8. Rational interpolation to |x| at the Chebyshev nodes.
    Brutman, Lev; Passow, Eli
    Bulletin of the Australian Mathematical Society, 1997, vol. 56, no. 1, pp. 81, Intenta.   
  9. Another note on polynomial vs. rational approximation.
    Shekhtman, Boris
    J. Approx. Theory 85 (1996), no. 3, 343--347.
  10. Uniform Rational Approximation  
    Liming Yang
    Proceedings of the American Mathematical Society, Vol. 123, No. 1. (Jan., 1995), pp. 201-206, Jstor.  
  11. Rational interpolation of the exponential function.
    Baratchart, L.; Saff, E. B.; Wielonsky, F.
    Canadian journal of mathematics, 1995, vol. 47, no. 6, pp. 1121, Intenta.  
  12. A modelling by rational approximations.
    Chocholat\'y, Pavol
    Rev. Anal. Numér. Théor. Approx. 23 (1994), no. 1, 55--62.
  13. Quadrature Formulas Based on Rational Interpolation  
    Walter Van Assche; Ingrid Vanherwegen
    Mathematics of Computation, Vol. 61, No. 204. (Oct., 1993), pp. 765-783, Jstor.  
  14. Behavior of alternation points in best rational approximation.
    Braess, D.; Lubinsky, D. S.; Saff, E. B.
    Rational approximation theory. Acta Appl. Math. 33 (1993), no. 2-3, 195--210.
  15. A rational approximation of the inverse normal probability function.
    Guirguis, G.H.
    Computational statistics & data analysis, 1991, vol. 11, no. 2, pp. 199, Intenta.   
  16. Quadrature formulas of interpolation type based on certain rational functions. (Spanish)
    González-Vera, Pablo; Santos León, Juan C.
    Proceedings of the XVth Portuguese-Spanish Conference on Mathematics, Vol. V (Portuguese) (Évora, 1990), 67--72, Univ. Évora, Évora, 1991, MathSciNet.  
  17. Existence of Hermite interpolatory end point constrained rational approximation.
    Lawson, J. D.; Lau, T. C.; Taylor, G. D.
    Utilitas Math. 38 (1990), 27--31.
  18. A Fast Algorithm for Rational Interpolation Via Orthogonal Polynomials  
    Omer Egecioglu; Cetin K. Koc  
    Mathematics of Computation, Vol. 53, No. 187. (Jul., 1989), pp. 249-264, Jstor.  
  19. A note on optimal interpolation with rational functions.
    Kilgore, Theodore
    Acta Sci. Math. (Szeged) 52 (1988), no. 1-2, 113--116, MathSciNet.  
  20. The interpolation methods of numerical integration and their connection with rational approximation. (Spanish)
    López Lagomasino, Guillermo; Illán González, Jesús
    Cienc. Mat. (Havana) 8 (1987), no. 2, 31--44.
  21. Some New Aspects of Rational Interpolation  
    Claus Schneider; Wilhelm Werner  
    Mathematics of Computation, Vol. 47, No. 175. (Jul., 1986), pp. 285-299, Jstor.  
  22. Résolution des équations à l'aide des fonctions rationnelles d'interpolation inverse. (French)
    [Solution of equations by means of inverse interpolation rational functions]
    Iancu, C.; Pavaloiu, I.
    Seminar of functional analysis and numerical methods, 71--78, Preprint, 85-1, Univ. "Babes-Bolyai", Cluj-Napoca, 1985, MathSciNet.  
  23. A Note on An Algorithm for Interpolating Rationals  
    Huang Yougun; Jack Williams  
    Mathematics of Computation, Vol. 42, No. 165. (Jan., 1984), pp. 111-113, Jstor.  
  24. Optimal relative error rational approximations to exp(x).
    Newman, D. J.
    J. Approx. Theory 40 (1984), no. 2, 111--114.
  25. The Caratheodory-Fejer Method for Real Rational Approximation  
    Lloyd N. Trefethen; Martin H. Gutknecht
    SIAM Journal on Numerical Analysis, Vol. 20, No. 2. (Apr., 1983), pp. 420-436, Jstor.  
  26. On Padé and best rational approximation.
    Borwein, Peter B.
    Canad. Math. Bull. 26 (1983), no. 1, 50--57.
  27. Rational Approximation to e-x and Related L2-Problems  
    Arnold Schonhage
    SIAM Journal on Numerical Analysis, Vol. 19, No. 5. (Oct., 1982), pp. 1067-1080, Jstor.  
  28. The Rational Approximation of Real Functions  
    Daniel E. Wulbert
    American Journal of Mathematics, Vol. 100, No. 6. (Dec., 1978), pp. 1281-1315, Jstor.  
  29. Rational Approximation to e-x .  II  
    Q. I. Rahman; G. Schmeisser
    Transactions of the American Mathematical Society, Vol. 235. (Jan., 1978), pp. 395-402.
  30. A Note on Best Uniform Rational Approximation  
    Binh Lam
    SIAM Journal on Numerical Analysis, Vol. 13, No. 6. (Dec., 1976), pp. 962-965, Jstor.  
  31. Chebyshev Approximation by Interpolating Rationals on [ 0, inf)  
    Charles B. Dunham
    Mathematics of Computation, Vol. 29, No. 130. (Apr., 1975), pp. 549-551, Jstor.  
  32. A Difficulty in Williams' Algorithm for Interpolating Rationals  
    Charles B. Dunham
    Mathematics of Computation, Vol. 29, No. 130. (Apr., 1975), pp. 552-553, Jstor.  
  33. On Some Aspects of the Rational Interpolation Problem  
    Luc Wuytack
    SIAM Journal on Numerical Analysis, Vol. 11, No. 1. (Mar., 1974), pp. 52-60, Jstor.  
  34. Existence Questions for the Problem of Chebyshev Approximation by Interpolating Rationals  
    G. D. Taylor; J. Williams
    Mathematics of Computation, Vol. 28, No. 128. (Oct., 1974), pp. 1097-1103, Jstor.  
  35. Numerical Chebyshev Approximation by Interpolating Rationals  
    Jack Williams
    Mathematics of Computation, Vol. 26, No. 117. (Jan., 1972), pp. 199-206, Jstor.
  36. Converse Theorems and Extensions in Chebyshev Rational Approximation to Certain Entire Functions in [ 0, + inf)  
    G. Meinardus; A. R. Reddy; G. D. Taylor; R. S. Varga  
    Transactions of the American Mathematical Society, Vol. 170. (Aug., 1972), pp. 171-185, Jstor.  
  37. Two Simple Algorithms for Discrete Rational Approximation  
    I. Barrodale; J. C. Mason
    Mathematics of Computation, Vol. 24, No. 112. (Oct., 1970), pp. 877-891, Jstor.   
  38. Constructive Techniques in Rational Approximation   
    T. W. Gamelin; J. Garnett  
    Transactions of the American Mathematical Society, Vol. 143. (Sep., 1969), pp. 187-200, Jstor.  
  39. On interpolation by rational functions.
    Bagby, Thomas
    Duke Math. J. 36 1969 95--104, MathSciNet.  
  40. A Rational Approximation to the Logarithm  
    R. P. Kelisky, T. J. Rivlin
    Mathematics of Computation, Vol. 22, No. 101. (Jan., 1968), pp. 128-136, Jstor.  
  41. Uniform Rational Approximation Using a Generalized Weight Function  
    D. G. Moursund; G. D. Taylor
    SIAM Journal on Numerical Analysis, Vol. 5, No. 4. (Dec., 1968), pp. 882-889, Jstor.  
  42. Interpolation and approximation by rational functions in the complex domain.
    Walsh, J. L.
    Fourth edition. American Mathematical Society Colloquium Publications, Vol. XX American Mathematical Society, Providence, R.I. 1965 x+405 pp., MathSciNet.  
  43. A Direct Method for Chebyshev Approximation by Rational Functions  
    Josef Stoer
    Journal of the ACM, Volume 11,  Issue 1, (January 1964), Pages: 59-69.  
  44. A direct method for Chebyshev approximation by rational functions.
    Stoer, Josef
    J. Assoc. Comput. Mach. 11 1964 59--69, MathSciNet.  
  45. Existence and Uniqueness of Interpolating Rational Functions  
    Nathaniel Macon, D. E. Dupree  
    American Mathematical Monthly, Vol. 69, No. 8. (Oct., 1962), pp. 751-759, Jstor.
  46. Note on Osculatory Rational Interpolation (in Technical Notes and Short Papers)  
    Herbert E. Salzer  
    Mathematics of Computation, Vol. 16, No. 80. (Oct., 1962), pp. 486-491, Jstor.  
  47. A Note on Rational Approximation  
    Robert W. Floyd
    Mathematics of Computation, Vol. 14, No. 69. (Jan., 1960), pp. 72-73, Jstor.  
  48. The Rational Approximation of Functions which are Formally Defined by a Power Series Expansion  
    P. Wynn  
    Mathematics of Computation, Vol. 14, No. 70. (Apr., 1960), pp. 147-186, Jstor.  
  49. An approximation method with rational functions.
    De Claris, Nick
    Tech. Rep. 287 Research Laboratory of Electronics, Massachusetts Institute of Technology, (1954), 27 pp., MathSciNet.  
  50. A note on approximation by rational functions.
    Kober, H.
    Bull. Amer. Math. Soc. 49, (1943). 437--443, MathSciNet.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004