Minimal shape-preserving projections onto Πn

Numerical Functional Analysis and Optimization

Volumn 18, Issue 5-6, 1997, Pages 507-520

  Chalmers, B L ^a   Prophet, M P ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b MURRAY STATE UNIVERSITY   (United States)

Author keywords

Minimal projections; Shape preserving

Indexed keywords

APPROXIMATION THEORY; ERROR ANALYSIS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; POLYNOMIALS;

SHAPE PRESERVING PROJECTION OPERATORS;

MATHEMATICAL OPERATORS;

EID: 0031188442     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1080/01630569708816775     Document Type: Article

References (18)

1. H. Berens and R. DeVore, A characterization of Bernstein polynomials, Approximation Theory III, E. W. Cheney, Ed., Academic Press, New York 1980, 213-219.
2. R. Bojanic and J. Roulier, Approximation of convex functions by convex splines and convexity preserving continuous linear operators, Anal. Numer. Theory Approx. 3(1974), 143-150.
3. B. L. Chalmers and F. T. Metcalf, A characterization and equations for minimal projections and extensions, J. Oper. Thy., 32(1994), 31-46..
4. B. L. Chalmers and F. T. Metcalf, Determination of a minimal projection from C[-1,1] onto the quadratics, Numer. Funct. Anal. and Optimiz., 11(1990), 1-10.
5. B. L. Chalmers and M. P. Prophet, The existence of shape-preserving operators with a given action, submitted.
6. B. L. Chalmers and G. D. Taylor, Uniform Approximation with constraints, Jber. d. Dt. Math.-Verein., 811979, 49-86.
7. G. Cross, Continuous linear transformations of n-convex functions, Real Analysis Exchange, 11(1985-86).
8. F. J. M. Delgado, Aproximacion conservativa con operadores polinomiales lineales, La Universidad de Granada, thesis, 1990 (available through Idaho State University Library, Pocatello, Idaho 83201).
9. R.A. DeVore, Monotone approximation by polynomials, SIAM J. Math. Anal. 8(1977), 906-921.
10. Z. Ditzian, D. Jiang and D. Leviatan, Shape preserving polynomial approximation in C[0, 1], Proc. Cambridge Phil. Soc. 112 (1992), 309-316.
11. N. Dunford and J. Schwartz, Linear Operators, Part I, Wiley-Interscience, New York, 1971.
12. Y. K. Hu, X. M. Yu and D. Leviatan, Convex polynomial and spline approximation in C[-1, 1], Constructive Approx. 10 (1994), 31-64.
13. D. Leviatan, Recent developments in shape preserving approximation, Proc. IDoMAT, 1995 (to appear).
14. p, Constr. Approx. 11 (1995), 299-320.
15. G. G. Lorentz and K. Zeller, Degree of approximation by monotone polynomials, I, J. Approx. Theory, 1(1968), 501-504.
16. I. Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Springer-Verlag, Berlin, 1970.
17. p spaces, Approx. Theory and Appl. 3(1987), 72-83.
18. 1-approximation, Proc. AMS, 103(1988), 1139-1146.