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Uniform approximation by Mc Callig rationals

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Abstract

Mc Callig considered ordinary rational functionsp/q on [0,α] or a finite subset with the denominatorq satisfying a normalization condition and having a lower bound. Existence of best uniform approximations and behavior of discretization are major topics of this paper. Characterization, uniqueness and denisty are also examined.

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References

  1. C. Dunham, Existence and continuity of the Chebyshev operator, SIAM Rev. 10 (1968) 444–446.

    Google Scholar 

  2. C. Dunham, Rational Chebyshev approximation on subsets, J. Approx. Theory 1 (1968) 484–487.

    Google Scholar 

  3. C. Dunham, Chebyshev approximation by families with the betweeness property, Trans. Amer. Math. Soc. 136 (1969) 151–157.

    Google Scholar 

  4. C. Dunham, Existence and continuity of the Chebyshev operator, II, in:Nonlinear Analysis and Applications, eds. S.P. Singh and J. H. Burry (Dekker, New York) pp. 403–412.

  5. C. Dunham, Chebyshev approximation by rationals with constrained denominators, J. Approx. Theory 37 (1983) 5–11.

    Google Scholar 

  6. C. Dunham, Chebyshev approximation by restricted rationals, Approx. Theory Appl. 1 (1985) 111–118.

    Google Scholar 

  7. C. Dunham, Non-density of restricted rationals, J. Approx. Theory 62 (1990) 145–146.

    Google Scholar 

  8. C. Dunham and J. Williams, Rate of convergence of discretization in Chebyshev approximation, Math. Comp. 37 (1981) 135–139.

    Google Scholar 

  9. E. Kaufman and G. Taylor, Uniform approximation by rational functions having restricted denominators, J. Approx. Theory 32 (1981) 9–26.

    Google Scholar 

  10. E. Kaufman, D. Leeming and G. Taylor, Uniform rational approximation by differential correction and Remez-differential correction, Int. J. Number. Meth. Eng. 17 (1981) 1273–1280.

    Google Scholar 

  11. J. Rice,The Approximation of Functions, Vol. 1 (Addision-Wesley, 1964).

  12. C. Zhu and C. Dunham, Existence and continuity of Chebyshev approximation with restraints, in:Approximation Theory and Applications, ed. S.P. Singh (Pitman, Boston, 1985) pp. 1–7.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, Canada

    Charles B. Dunham

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  1. Charles B. Dunham
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Communicated by M.H. Gutknecht

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Dunham, C.B. Uniform approximation by Mc Callig rationals. Numer Algor 7, 201–204 (1994). https://doi.org/10.1007/BF02140683

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  • DOI: https://doi.org/10.1007/BF02140683

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