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The Limit of Biased Varisolvent Chebyshev Approximation

Published online by Cambridge University Press:  20 November 2018

Charles B. Dunham
Charles B. Dunham*
Affiliation:
Computer Science Department University of Western Ontario, LondonOntario N6A 5B9 Canada
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Abstract

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Best biased and one-sided Chebyshev approximation with respect to a varisolvent approximating function on an interval are considered. The uniform limit of best biased approximations is the (unique) best one-sided approximation if the best one-sided approximation is of maximum degree. Examples are given where the best one-sided approximation is not of maximum degree and failure of uniform convergence and of existence occurs.

Keywords

41A50
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 1 , 01 March 1982 , pp. 54 - 58
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Barrar, R. and Loeb, H., On N-parameter and unisolvent families, J. Approx. Theory 1 (1968), 180-181.Google Scholar
2. Barrar, R. and Loeb, H., On the continuity of the nonlinear Tschebyscheft operator,Pac. J. Math 32 (1970), 593-601.Google Scholar
3. Dunham, C., Necessity of alternation, Can. Math. Bull. 11 (1968), 743-744.Google Scholar
4. Dunham, C., Continuity of the varisolvent Chebyshev operator, Bull. Amer. Math. Soc. 74 (1968), 606-608.Google Scholar
5. Dunham, C., Chebyshev approximation with respect to a weight function, J. Approx. Theory 2 (1969), 223-232.Google Scholar
6. Dunham, C., Alternating minimax approximation with unequal restraints, J. Approx. Theory 10 (1974), 199-205.Google Scholar
7. Dunham, C., Alternating Chebyshev approximation, Trans. Amer. Math. Soc. 178 (1973), 95-109.Google Scholar
8. Meinardus, G. and Schwedt, D., Nicht-lineare approximationen, Arch. Rat. Mech. Anal. 17 (1964), 297-326.Google Scholar
9. Rice, J., The Approximation of Functions, Volume 2, Addison-Wesley, Reading, Mass., 1969.Google Scholar