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Darst, R. B.; Legg, D. A.; Townsend, D. W.

The Polya algorithm in \(L_ \infty\) approximation. (English) Zbl 0519.41027

J. Approximation Theory 38, 209-220 (1983).
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Cited in 6 Documents

MSC:

41A50 Best approximation, Chebyshev systems
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
65D15 Algorithms for approximation of functions

Keywords:

Polya algorithm; non-decreasing functions; uniformly convex Banach space

Citations:

Zbl 0461.41023
Cite Review PDF
Full Text: DOI

References:

[1] Chui, C. K.; Smith, P. W.; Ward, J. D., Favard’s solution is the limit of \(W^{k, p} \)-splines, Trans. Amer. Math. Soc., 220, 299-305 (1976) · Zbl 0337.41012
[2] Darst, R. B., Convergence of \(L_p\) approximations as \(p\) → ∞, (Proc. Amer. Math. Soc., 81 (1981)), 433-436 · Zbl 0461.41023
[3] Darst, R. B.; Sahab, S., Approximation of continuous and quasi-continuous functions by monotone functions, J. Approx. Theory, 38, 9-27 (1983)
[4] Dunford, N.; Schwartz, J., Linear Operators Part I (1958), Interscience: Interscience New York · Zbl 0084.10402
[5] Holmes, R. B., A Course on Optimization and Best Approximation, (Lecture Notes in Mathematics No. 257 (1972), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York) · Zbl 0234.46016
[6] Landers, D.; Rogge, L., On Projections and monotony in \(L_p\)-spaces, Manuscripta Math., 26, 363-369 (1979) · Zbl 0393.46026
[7] Landers, D.; Rogge, L., Isotonic approximation in \(L_s\), J. Approx. Theory, 21, 199-223 (1981) · Zbl 0467.41014
[8] Rice, J., (The Approximation of Functions, Vol. I (1964), Addison-Wesley: Addison-Wesley Reading, Mass) · Zbl 0114.27001
[9] Rice, J., (The Approximation of Functions, Vol. II (1969), Addison-Wesley: Addison-Wesley Reading, Mass) · Zbl 0185.30601
[10] Ubhaya, V. A., Isotone Optimization, II, J. Approx. Theory, 12, 315-331 (1974) · Zbl 0292.41026
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