Bibliography for the Rational Approximation

unabridged

 

  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. Hermite-type Interpolation Formula for Rational Function Interpolation Problem With Prescribed Poles
    Zhenghong, Y.
    Journal- China Agricultural University, 2002, vol. 7, no. 6, pp. 1-4, Intenta.   
  4. 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.
  5. Spline-form matrix valued rational interpolation
    Yang, S.-l.
    Journal- Suzhou University Natural Science, 2001, vol. 17, no. 3, pp. 7-11, Intenta.   
  6. On hybrid rational function approximation and stabilization theory through interval calculus. (Japanese)
    Murakami, Yumi; Kai, Hiroshi; Noda, Matu-Tarow
    Computer algebra---algorithms, implementations and applications (Kyoto, 2001).  Surikaisekikenkyusho Kokyuroku  No. 1295 (2002), 197--202, MathSciNet.  
  7. Interpolation by Rational Fuctions with Nodes on the Unit Circle.
    Bultheel, Adhemar; González-Vera, Pablo; Hendriksen, Erik; Njåstad, Olav
    Acta Applicandae Mathematicae, 2000, vol. 61, no. 1/3, pp. 101-118, Intenta.   
  8. Rational approximation with varying weights. III.
    Saff, E. B.; Simeonov, P. C.
    J. Approx. Theory 102 (2000), no. 2, 341--362.
  9. Hybrid Rational Function Approximation and Its Accuracy Analysis
    Kai, H.; Noda, M.-T.
    Reliable Computing, 2000, vol. 6, no. 4, pp. 429-438, Intenta.   
  10. Thiele Rational Interpolation for the Numerical Computation of the Reversible Randles-Sevcik Function in Electrochemistry.
    Lether, Frank G.
    Journal of Scientific Computing, 1999, vol. 14, no. 3, pp. 259, Intenta.  
  11. 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.  
  12. Error estimation of hybrid rational function approximation. (Japanese)
    Kai, Hiroshi
    Trans. Inform. Process. Soc. Japan 40 (1999), no. 4, 1754--1759, MathSciNet.  
  13. A note on rational approximations.
    Adiga, Chandrashekar; Vasuki, K. R.
    J. Indian Math. Soc. (N.S.) 65 (1998), no. 1-4, 181--189.
  14. Orthogonal rational functions and interpolatory product rules on the unit circle. I.
    Bultheel, A.; González-Vera, P.; Hendriksen, E.; Njåstad, O.
    Recurrence and interpolation. Analysis (Munich) 18 (1998), no. 2, 167--183, MathSciNet.  
  15. Low degree rational spline interpolation.
    Oja, P.
    BIT, 1997, vol. 37, no. 4, pp. 901, Intenta.   
  16. 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.   
  17. An algorithm for interpolation with positive rational functions on the imaginary axis.
    Mosquera, Carlos; Pérez, Fernando
    Automatica J. IFAC 33 (1997), no. 12, 2277--2280, MathSciNet.  
  18. Interpolation of piecewise-analytic functions by rational functions. (Russian)
    Rovba, E. A.
    Vestsi Akad. Navuk Belarusi Ser. Fi z.-Mat. Navuk 1997, no. 2, 11--15, 139, MathSciNet.  
  19. Another note on polynomial vs. rational approximation.
    Shekhtman, Boris
    J. Approx. Theory 85 (1996), no. 3, 343--347.
  20. Convergence of interpolation sequences of rational functions with preassigned poles (extended abstract). (Chinese)
    Zhu, Lai Yi; Gao, Shi Chen
    J. Math. Res. Exposition 16 (1996), no. 3, 410--412, MathSciNet.  
  21. Uniform Rational Approximation  
    Liming Yang
    Proceedings of the American Mathematical Society, Vol. 123, No. 1. (Jan., 1995), pp. 201-206, Jstor.  
  22. On rational approximations of functions.
    Kalaida, O. F.
    J. Math. Sci. 75 (1995), no. 4, 1807--1811.
  23. 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.  
  24. On the orthogonal rational functions with arbitrary poles and interpolation properties.
    Pan, K.
    J. Comput. Appl. Math. 60 (1995), no. 3, 347--355, MathSciNet.  
  25. Interpolation properties of rational functions of best approximation in the mean square on the circle and in the disk. (Russian)
    Vyacheslavov, N. S.; Ramazanov, A. K.
    Mat. Zametki 57 (1995), no. 2, 228--239, 318; translation in Math. Notes 57 (1995), no. 1-2, 158--166, MathSciNet.  
  26. A modelling by rational approximations.
    Chocholat\'y, Pavol
    Rev. Anal. Numér. Théor. Approx. 23 (1994), no. 1, 55--62.
  27. The linearized Remes algorithm for rational approximation. (Chinese)
    Xiong, Gui Jing; Wei, Dan
    Numer. Math. J. Chinese Univ. 16 (1994), no. 2, 126--133.
  28. Quadrature Formulas Based on Rational Interpolation  
    Walter Van Assche; Ingrid Vanherwegen
    Mathematics of Computation, Vol. 61, No. 204. (Oct., 1993), pp. 765-783, Jstor.  
  29. 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.
  30. Rational Interpolation via Orthogonal Polynomials.
    Gemignani, L.
    Computers & mathematics with applications, 1993, vol. 26, no. 5, pp. 27, Intenta.   
  31. A parallel algorithm for discrete least squares rational approximation.
    Van Barel, Marc; Bultheel, Adhemar
    Numer. Math. 63 (1992), no. 1, 99--121.
  32. On the rate of rational approximation of the function exp(-x) on the positive semi-axis.
    Finkelstein, A. Martines
    Moscow University mathematics bulletin, 1991, vol. 46, no. 6, pp. 65, Intenta.   
  33. A rational approximation of the inverse normal probability function.
    Guirguis, G.H.
    Computational statistics & data analysis, 1991, vol. 11, no. 2, pp. 199, Intenta.   
  34. A rational displacement interpolation function for axisymmetric finite element analysis of nearly incompressible materials.
    Yu, H.S.
    Finite elements in analysis and design, 1991, vol. 10, no. 3, pp. 205, Intenta.  
  35. The convergence problem for interpolation sequences of rational functions in the unit disk. (Chinese)
    Shen, Xie Chang
    Acta Math. Sinica 34 (1991), no. 6, 851--858, MathSciNet.  
  36. 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.  
  37. Existence of Hermite interpolatory end point constrained rational approximation.
    Lawson, J. D.; Lau, T. C.; Taylor, G. D.
    Utilitas Math. 38 (1990), 27--31.
  38. Interpolation of sparse rational functions without knowing bounds on exponents.
    Grigoriev, Dima Yu.; Karpinski, Marek; Singer, Michael F.
    31st Annual Symposium on Foundations of Computer Science, Vol. I, II (St. Louis, MO, 1990), 840--846, IEEE Comput. Soc. Press, Los Alamitos, CA, 1990, MathSciNet.  
  39. On interpolation by rational functions with prescribed poles with applications to multivariate interpolation.
    Mühlbach, G.
    Extrapolation and rational approximation (Luminy, 1989). J. Comput. Appl. Math. 32 (1990), no. 1-2, 203--216, MathSciNet.  
  40. 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.  
  41. A note on optimal interpolation with rational functions.
    Kilgore, Theodore
    Acta Sci. Math. (Szeged) 52 (1988), no. 1-2, 113--116, MathSciNet.  
  42. Rational functions for guaranteed and experimentally well-conditioned global interpolation.
    Berrut, J.-P.
    Comput. Math. Appl. 15 (1988), no. 1, 1--16, MathSciNet.  
  43. 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.
  44. On interpolation of holomorphic functions by rational functions.  
    Kloke, Helmut
    Complex Variables Theory Appl.  8  (1987),  no. 1-2, 41--54, MathSciNet.  
  45. Some New Aspects of Rational Interpolation  
    Claus Schneider; Wilhelm Werner  
    Mathematics of Computation, Vol. 47, No. 175. (Jul., 1986), pp. 285-299, Jstor.  
  46. 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.  
  47. 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.  
  48. Optimal relative error rational approximations to exp(x).
    Newman, D. J.
    J. Approx. Theory 40 (1984), no. 2, 111--114.
  49. The generalized Padé rational approximation to trigonometric series. (Chinese)
    Cheng, Qian Sheng
    Math. Numer. Sinica 6 (1984), no. 2, 182--193.
  50. Padé and rational approximations to systems of functions and their arithmetic applications.
    Chudnovsky, D. V.; Chudnovsky, G. V.
    Number theory (New York, 1982), 37--84, Lecture Notes in Math., 1052, Springer, Berlin, 1984.
  51. Some properties and applications of Chebyshev polynomial and rational approximation.
    Mason, J. C.
    Rational approximation and interpolation (Tampa, Fla., 1983), 27--48, Lecture Notes in Math., 1105, Springer, Berlin, 1984.
  52. 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.  
  53. Discrete Lp approximation by rational functions.
    Watson, G. A.
    Rational approximation and interpolation (Tampa, Fla., 1983), 489--501, Lecture Notes in Math., 1105, Springer, Berlin, 1984, MathSciNet.  
  54. Frequency fitting of rational approximations to the exponential functions.
    Iserles, A.; Nørsett, S. P.
    Math. Comp. 40 (1983), no. 162, 547--559.
  55. On Padé and best rational approximation.
    Borwein, Peter B.
    Canad. Math. Bull. 26 (1983), no. 1, 50--57.
  56. 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.  
  57. Interpolation by rational functions. (Russian)
    Orudzhev, G. A.
    Izv. Vyssh. Uchebn. Zaved. Mat. 1981, no. 8, 74--77, MathSciNet.  
  58. The Rational Approximation of Real Functions  
    Daniel E. Wulbert
    American Journal of Mathematics, Vol. 100, No. 6. (Dec., 1978), pp. 1281-1315, Jstor.  
  59. Rational Approximation to e-x .  II  
    Q. I. Rahman; G. Schmeisser
    Transactions of the American Mathematical Society, Vol. 235. (Jan., 1978), pp. 395-402.
  60. Approximation with a class of rational functions.
    van Hulzen, J. A.; Hettich, R. P.
    Information processing 77 (Proc. IFIP Congr., Toronto, Ont., 1977), pp. 487--492. IFIP Congr. Ser., Vol. 7, North-Holland, Amsterdam, 1977, MathSciNet.
  61. A Note on Best Uniform Rational Approximation  
    Binh Lam
    SIAM Journal on Numerical Analysis, Vol. 13, No. 6. (Dec., 1976), pp. 962-965, Jstor.  
  62. Chebyshev Approximation by Interpolating Rationals on [ 0, inf)  
    Charles B. Dunham
    Mathematics of Computation, Vol. 29, No. 130. (Apr., 1975), pp. 549-551, Jstor.  
  63. A Difficulty in Williams' Algorithm for Interpolating Rationals  
    Charles B. Dunham
    Mathematics of Computation, Vol. 29, No. 130. (Apr., 1975), pp. 552-553, Jstor.  
  64. 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.  
  65. Hermite interpolation by generalized rational functions.
    Mäkelä, Matti; Nevanlinna, Olavi; Sipilä, Aarne H.
    Ann. Acad. Sci. Fenn. Ser. A I No. 564 (1974), 10 pp., MathSciNet.  
  66. 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.  
  67. Numerical Chebyshev Approximation by Interpolating Rationals  
    Jack Williams
    Mathematics of Computation, Vol. 26, No. 117. (Jan., 1972), pp. 199-206, Jstor.
  68. 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.  
  69. 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.   
  70. Constructive Techniques in Rational Approximation   
    T. W. Gamelin; J. Garnett  
    Transactions of the American Mathematical Society, Vol. 143. (Sep., 1969), pp. 187-200, Jstor.  
  71. On interpolation by rational functions.
    Bagby, Thomas
    Duke Math. J. 36 1969 95--104, MathSciNet.  
  72. 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.  
  73. 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.  
  74. 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.  
  75. A Direct Method for Chebyshev Approximation by Rational Functions  
    Josef Stoer
    Journal of the ACM, Volume 11,  Issue 1, (January 1964), Pages: 59-69.  
  76. A direct method for Chebyshev approximation by rational functions.
    Stoer, Josef
    J. Assoc. Comput. Mach. 11 1964 59--69, MathSciNet.  
  77. 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.
  78. 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.  
  79. A Note on Rational Approximation  
    Robert W. Floyd
    Mathematics of Computation, Vol. 14, No. 69. (Jan., 1960), pp. 72-73, Jstor.  
  80. 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.  
  81. An approximation method with rational functions.
    De Claris, Nick
    Tech. Rep. 287 Research Laboratory of Electronics, Massachusetts Institute of Technology, (1954), 27 pp., MathSciNet.  
  82. A note on approximation by rational functions.
    Kober, H.
    Bull. Amer. Math. Soc. 49, (1943). 437--443, MathSciNet.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004