Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Some new aspects of rational interpolation

Authors: Claus Schneider and Wilhelm Werner
Journal: Math. Comp. 47 (1986), 285-299
MSC: Primary 65D05; Secondary 41A20
MathSciNet review: 842136
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A new algorithm for rational interpolation based on the barycentric formula is developed; the barycentric representation of the rational interpolation function possesses various advantages in comparison with other representations such as continued fractions: it provides, e.g., information concerning the existence and location of poles of the interpolant.

References [Enhancements On Off] (What's this?)

  • [1] A.-L. Cauchy, "Sur la formule de Lagrange relative à l'interpolation," Cours d'Analyse de l'Ecole Royale Polytéchnique (Analyse Algébrique), Note V, Paris, 1821, pp. 429-433, reprinted in: Oeuvres, sér. 2, Vol. III, 1897.
  • [2] P. R. Graves-Morris, Efficient reliable rational interpolation, Padé approximation and its applications, Amsterdam 1980 (Amsterdam, 1980), Lecture Notes in Math., vol. 888, Springer, Berlin-New York, 1981, pp. 28–63. MR 649084
  • [3] Peter Henrici, Applied and computational complex analysis, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Volume 1: Power series—integration—conformal mapping—location of zeros; Pure and Applied Mathematics. MR 0372162
  • [4] L. Kronecker, "Zur Theorie der Elimination einer Variablen aus zwei algebraischen Gleichungen," Monatsher. Königl. Preuss. Akad. Wiss. Berlin, 1881, pp. 535-600.
  • [5] H. Maehly and Ch. Witzgall, Tschebyscheff-Approximationen in kleinen Intervallen. II. Stetigkeitssätze für gebrochen rationale Approximationen, Numer. Math. 2 (1960), 293–307 (German). MR 0126107
  • [6] J. Meinguet, On the solubility of the Cauchy interpolation problem, Approximation Theory (Proc. Sympos., Lancaster, 1969) Academic Press, London, 1970, pp. 137–163. MR 0270028
  • [7] L. M. Milne-Thomson, The Calculus of Finite Differences, Macmillan and Co., Ltd., London, 1951. MR 0043339
  • [8] G. Opitz, Steigungsmatrizen, Z. Angew. Math. Mech. 44 (1964), T52–T54 (German). MR 0185806
  • [9] Arno Predonzan, Su una formula d’interpolazione per le funzioni razionali, Rend. Sem. Mat. Univ. Padova 22 (1953), 417–425 (Italian). MR 0057937
  • [10] H. E. Salzer, Rational interpolation using incomplete barycentric forms, Z. Angew. Math. Mech. 61 (1981), no. 3, 161–164 (English, with German and Russian summaries). MR 626019, 10.1002/zamm.19810610304
  • [11] Helmut Werner and Robert Schaback, Praktische Mathematik. II, Second, revised and enlarged edition, Springer-Verlag, Berlin-New York, 1979 (German). Based on lectures at the Universities of Münster and Göttingen; Hochschultext; Edited by J. Ebert. MR 520918
  • [12] Helmut Werner, Rationale Tschebyscheff-Approximation, Eigenwerttheorie und Differenzenrechnung, Arch. Rational Mech. Anal. 13 (1963), 330–347 (German). MR 0154025
  • [13] H. Werner, A reliable method for rational interpolation, Padé approximation and its applications (Proc. Conf., Univ. Antwerp, Antwerp, 1979) Lecture Notes in Math., vol. 765, Springer, Berlin, 1979, pp. 257–277. MR 561455
  • [14] Helmut Werner, Ein Algorithmus zur rationalen Interpolation, Numerical methods of approximation theory, Vol. 5 (Conf., Math. Res. Inst., Oberwolfach, 1979) Internat. Ser. Numer. Math., vol. 52, Birkhäuser, Basel-Boston, Mass., 1980, pp. 319–337 (German, with English summary). MR 573777
  • [15] H. Werner, A reliable and numerically stable program for rational interpolation of Lagrange data, Computing 31 (1983), no. 3, 269–286 (English, with German summary). MR 722327, 10.1007/BF02263437
  • [16] Wilhelm Werner, Polynomial interpolation: Lagrange versus Newton, Math. Comp. 43 (1984), no. 167, 205–217. MR 744931, 10.1090/S0025-5718-1984-0744931-0
  • [17] Luc Wuytack, On some aspects of the rational interpolation problem, SIAM J. Numer. Anal. 11 (1974), 52–60. MR 0340890

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D05, 41A20

Retrieve articles in all journals with MSC: 65D05, 41A20

Additional Information

Article copyright: © Copyright 1986 American Mathematical Society