Best comonotone approximation
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- by Frank Deutsch and Jun Zhong PDF
- Trans. Amer. Math. Soc. 344 (1994), 617-627 Request permission
Abstract:
A general theory of best comonotone approximation in $C[a,b]$ by elements of an n-dimensional extended Chebyshev subspace is described. In particular, theorems on the existence, (in general) nonuniqueness, and characterization of best comonotone approximations are established.References
- E. W. Cheney, Introduction to approximation theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0222517
- F. R. Deutsch and P. H. Maserick, Applications of the Hahn-Banach theorem in approximation theory, SIAM Rev. 9 (1967), 516–530. MR 216224, DOI 10.1137/1009072
- Charles B. Dunham, Chebyshev approximation by families with the betweeness property, Trans. Amer. Math. Soc. 136 (1969), 151–157. MR 236585, DOI 10.1090/S0002-9947-1969-0236585-5
- G. G. Lorentz and K. L. Zeller, Monotone approximation by algebraic polynomials, Trans. Amer. Math. Soc. 149 (1970), 1–18. MR 285843, DOI 10.1090/S0002-9947-1970-0285843-5
- R. A. Lorentz, Uniqueness of best approximation by monotone polynomials, J. Approximation Theory 4 (1971), 401–418. MR 291688, DOI 10.1016/0021-9045(71)90006-2
- D. J. Newman, Efficient co-monotone approximation, J. Approx. Theory 25 (1979), no. 3, 189–192. MR 531408, DOI 10.1016/0021-9045(79)90009-1
- D. J. Newman, Eli Passow, and Louis Raymon, Piecewise monotone polynomial approximation, Trans. Amer. Math. Soc. 172 (1972), 465–472. MR 310506, DOI 10.1090/S0002-9947-1972-0310506-9
- E. Passow and L. Raymon, Monotone and comonotone approximation, Proc. Amer. Math. Soc. 42 (1974), 390–394. MR 336176, DOI 10.1090/S0002-9939-1974-0336176-9
- Eli Passow, Louis Raymon, and John A. Roulier, Comonotone polynomial approximation, J. Approximation Theory 11 (1974), 221–224. MR 352807, DOI 10.1016/0021-9045(74)90013-6
- Louis Raymon, Comonotone approximation and piecewise monotone interpolation, Theory of approximation, with applications (Proc. Conf., Univ. Calgary, Calgary, Alta., 1975; dedicated to the memory of Eckard Schmidt), Academic Press, New York, 1976, pp. 220–237. MR 0412676
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 344 (1994), 617-627
- MSC: Primary 41A50; Secondary 41A65
- DOI: https://doi.org/10.1090/S0002-9947-1994-1260201-1
- MathSciNet review: 1260201