Skip to main content
SpringerLink
Log in

Biased rational chebyshev approximation

  • Scientific Notes
  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

Chebyshev approximation on an interval [α, β] by ordinary rational functions when positive deviations (errors) are magnified by a bias factor is considered. This problem is related to one-sided Chebyshev approximation for large bias factors. Best approximations are characterized by alternation. Non-degenerate best approximations can be determined by the Remez algorithm. A variant of the Fraser-Hart-Remez algorithm is implemented.

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. W. J. Cody, W. Fraser and J. F. Hart,Rational Chebyshev approximation using linear equations, Numer. Math. 12 (1968), 242–251.

    Google Scholar 

  2. C. Dunham,Transformed rational Chebyshev approximation II, Numer. Math. 12 (1968), 8–10.

    Google Scholar 

  3. C. Dunham,Chebyshev approximation with respect to a weight function, J. Approx. Theory 2 (1969), 223–232.

    Google Scholar 

  4. C. Dunham,Convergence of the Fraser-Hart algorithm for rational Chebyshev approximation, Math. Comp. 29 (1975), 1078–1082.

    Google Scholar 

  5. C. Dunham,The limit of biased varisolvent Chebyshev approximation, Canad. Math. Bull., accepted.

  6. W. Fraser and J. F. Hart,On the computation of rational approximations to continuous functions, Comm. ACM 5 (1962), 401–403, 414.

    Google Scholar 

  7. G. Meinardus,Approximation of Functions, Springer-Verlag, New York, 1967.

    Google Scholar 

  8. A. Young and E. A. Kiountouzis,Best approximation in an asymmetrically weighted L 1 measure, J. Inst. Maths. Appl. 24 (1979), 379–394.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, University of Western Ontario, N6A 5B9, London, Ontario, Canada

    Charles B. Dunham

Authors
  1. Charles B. Dunham
    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

Dunham, C.B. Biased rational chebyshev approximation. BIT 22, 119–122 (1982). https://doi.org/10.1007/BF01934401

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01934401

Keywords

Search

Navigation