Skip to main content
SpringerLink
Log in

An Interval Polynomial Interpolation Problem and Its Lagrange Solution

  • Published:
Reliable Computing

Abstract

In many practical problems, we need to use interpolation: we know that the value of a quantity is uniquely determined by some other quantity x (i.e., y = f(x)), we have measured several pairs of values (xi, yi), and we want to predict y for a given x. We can only guarantee estimates for y if we have some a priori information about the function f(x). In particular, in some problems, we know that f(x) is a polynomial of known degree d (e.g., that it is linear, or that it is quadratic). For this polynomial interpolation, with interval uncertainty of the input data (xi, yi), we present several reasonable algorithms that compute, for a given x0, guaranteed bounds for f(x0).

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. Alefeld, G. and Herzberger, J.: Introduction to Interval Computations, Academic Press, New York, 1983.

    Google Scholar 

  2. Crane, M. A.: A Bounding Technique for Polynomial Functions, SIAM J. Appl. Math. 29(4) (1975), pp. 751-754.

    Google Scholar 

  3. Gaganov, A. A.: Computational Complexity of the Range of the Polynomial in Several Variables, Cybernetics (1985), pp. 418-421.

  4. Garey, M. R. and Johnson, D. S.: Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.

    Google Scholar 

  5. Gerald, G. F. and Wheatly, P. O.: Applied Numerical Analysis, 5th edition, Addison-Wesley, 1994.

  6. Herzberger, J.: Note on a Bounding Technique for Polynomial Functions, SIAM J. Appl. Math. 34(4) (1978), pp. 685-686.

    Google Scholar 

  7. Kearfott, R. B., Dawande, M., Du, K., and Hu, C.: Algorithm 737: INTLIB: A Portable Fortran-77 Interval Standard-Function Library, ACM Transactions on Mathematical Software 20(4) (1994), pp. 447-459.

    Google Scholar 

  8. Kincaid, D. and Cheney, W.: Numerical Analysis, Brooks/Cole, 1990.

  9. Kreinovich, V. and Bernat, A.: Parallel Algorithms for Interval Computations: An Introduction, Interval Computations 3 (1994), pp. 6-63.

    Google Scholar 

  10. Markov, S. M.: Some Interpolation Problems Involving Interval Data, Interval Computations 3 (1993), pp. 164-182.

    Google Scholar 

  11. Moore, R. E.: Methods and Applications of Interval Analysis, SIAM, 1979.

Download references

Author information

Authors and Affiliations

  1. Department of Computer and Mathematical Sciences, University of Houston-Downtown, Houston, Texas, 77002, USA

    Chenyi Hu, Angelina Cardenas, Stephanie Hoogendoorn & Pedro Sepulveda Jr.

Authors
  1. Chenyi Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Angelina Cardenas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stephanie Hoogendoorn
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pedro Sepulveda Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chenyi Hu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hu, C., Cardenas, A., Hoogendoorn, S. et al. An Interval Polynomial Interpolation Problem and Its Lagrange Solution. Reliable Computing 4, 27–38 (1998). https://doi.org/10.1023/A:1009946531786

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009946531786

Keywords

Search

Navigation