Skip to main content
SpringerLink
Log in

Multivariate rational data fitting: general data structure, maximal accuracy and object orientation

  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

Sections 1 and 2 discuss the advantages of an object-oriented implementation combined with higher floating-point arithmetic, of the algorithms available for multivariate data fitting using rational functions. Section 1 will in particular explain what we mean by “higher arithmetic”. Section 2 will concentrate on the concepts of “object orientation”. In sections 3 and 4 we shall describe the generality of the data structure that can be dealt with: due to some new results virtually every data set is acceptable right now, with possible coalescence of coordinates or points. In order to solve the multivariate rational interpolation problem the data sets are fed to different algorithms depending on the structure of the interpolation points in then-variate space.

This text is a preparatory publication for the development of a scientific expert system for multivariate rational interpolation. The issues addressed are relevant to the implementation of such a system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Abouir and A. Cuyt, Multivariate partial Newton-Padé and Newton-Padé type approximants, J. Approx. Th. (to appear).

  2. Acrith-XSC: IBM High Accuracy Arithmetic — Extended Scientific Computation. Version 1, Release 1, IBM Deutschland GmbH, Department 3282, Böblingen.

  3. ARITHMOS (BS2000): Benutzerhandbuch, SIEMENS AG, Bereich Datentechnik.

  4. H. Arndt, Ein verallgemeinter Kettenbruch-Algorithmus zur rationalen Hermite-Interpolation. Numer. Math. 36 (1980) 99–107.

    Article  Google Scholar 

  5. C. Brezinski, A general extrapolation algorithm, Numer. Math. 35 (1980) 175–187.

    Article  Google Scholar 

  6. A. Cuyt, A recursive computation scheme for multivariate rational interpolants, SIAM J. Num. Anal. 24 (1987) 228–238.

    Article  Google Scholar 

  7. A. Cuyt, Extension of “A multivariate convergence theorem of the de Montessus de Ballore type” to multipoles, J. Comp. Appl. Math. 41 (1992) 323–330.

    Article  Google Scholar 

  8. A. Cuyt, Multivariate rational interpolation: old and new results, in preparation.

  9. A. Cuyt and B. Verdonk, General order Newton-Padé approximants for multivariate functions, Numer. Math. 43 (1984) 293–307.

    Article  Google Scholar 

  10. A. Cuyt and B. Verdonk, Different techniques for the construction of multivariate rational interpolants, in:Nonlinear Numerical Methods and Rational Approximation, ed. A. Cuyt (1988) pp. 167–190.

  11. A. Cuyt and B. Verdonk, Evaluation of branched continued fractions using block-tridiagonal linear systems, IMA J. Numer. Anal. 8 (1988) 209–217.

    Google Scholar 

  12. C. Falcó Korn, S. Gutzwiller, S. König and Ch. Ullrich, Modula-SC. Motivation, language definition and implementation, IMACS Ann. Comput. Appl. Math. 12 (1992) 161–179.

    Google Scholar 

  13. FORTRAN for scientific computation. Language description and sample programs, Institute for Applied Mathematics, University of Karlsruhe.

  14. D. Goldberg, What every computer scientist should know about floating-point arithmetic, ACM Comp. Surv. 23 (1991) 5–48.

    Article  Google Scholar 

  15. P. Graves-Morris, Practical, reliable, rational interpolation, J. Inst. Math. Appl. 25 (1980) 267–286.

    Google Scholar 

  16. W. Krämer, Highly accurate evaluation of program parts with applications, IMACS Ann. Comput. Appl. Math. 7 (1990) 397–409.

    Google Scholar 

  17. U. Kulisch (ed.),Pascal-SC: Information Manual and Floppy Disks (Wiley-Teubner, Stuttgart, 1987).

    Google Scholar 

  18. U. Kulisch and W. Miranker,Computer Arithmetic in Theory and Practice (Academic Press, New York, 1981).

    Google Scholar 

  19. U. Kulisch and W. Miranker, The arithmetic of the digital computer: a new approach, SIAM Rev. 28 (1986) 1–36.

    Article  Google Scholar 

  20. C. Lawo, C-XSC, A programming environment for eXtended Scientific Computation,Proc. 13th IMACS World Congress, vol. 1 (1991) p. 34.

    Google Scholar 

  21. J. Miklosko, Investigation of algorithms for numerical computation of continued fractions, USSR Comp. Math. Math. Phys. 16 (1976) 1–12.

    Article  Google Scholar 

  22. Ch. Ullrich and J. Wolff von Gudenberg (eds.),Accurate Numerical Algorithms: A Collection of Research Papers (Springer, Berlin, 1989).

    Google Scholar 

  23. J. Wolff von Gudenberg, Object-oriented concepts for scientific computation, IMACS Ann. Comput. Appl. Math. 12 (1992) 181–192.

    Google Scholar 

  24. R. Klatte, V. Kulisch, M. Neaga, D. Ratz and C. Ullrich (eds.),Pascal-XSC. Language Reference with Examples (Springer, Berlin, 1992).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Universiteit Antwerpen (UIA), Universiteitsplein 1, B-2610, Wilrijk-Antwerpen, Belgium

    Annie Cuyt (Brigitte Verdonk) & Brigitte Verdonk

Authors
  1. Annie Cuyt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Brigitte Verdonk
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cuyt, A., Verdonk, B. Multivariate rational data fitting: general data structure, maximal accuracy and object orientation. Numer Algor 3, 159–172 (1992). https://doi.org/10.1007/BF02141925

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02141925

Keywords

Search

Navigation