An upper bound on the approximation power of principal shift-invariant spaces

Constructive Approximation

Volumn 13, Issue 2, 1997, Pages 155-176

  Johnson, M J ^a  

^a KUWAIT UNIVERSITY   (Kuwait)

Author keywords

Approximation order; Approximation power; Shift invariant spaces; Strang Fix conditions

Indexed keywords

EID: 0031536525     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02678462     Document Type: Article

References (27)

1. M. ABRAMOWITZ, I. A. STEGUN (1970): Handbook of Mathematical Functions. New York: Dover.
2. R. K. BEATSON, W. A. LIGHT (1992): Quasi-interpolation in the absence of polynomial reproduction. In: Numerical Methods of Approximation Theory (D. Braess, L. L. Schumaker, eds.). Boston: Birkhäuser-Verlag, pp. 21-39.
3. C. DE BOOR, R. A. DEVORE (1983): Approximation by smooth multivariate splines. Trans. Amer. Math. Soc., 276:775-788.
4. d). Trans. Amer. Math. Soc.
5. C. DE BOOR, K. HÖLLIG (1982/3): B-splines from parallelepipeds. J. Analyse Math., 42:99-115.
6. C. DE BOOR, K. HÖLLIG, S. RIEMENSCHNEIDER (1993): Box Splines. New York: Springer-Verlag.
7. C. DE BOOR, R.-Q. JIA (1985): Controlled approximation and a characterization of the local approximation order. Proc. Amer. Math. Soc., 95:547-553.
8. C. DE BOOR, A. RON (1992): Fourier analysis of approximation orders from principal shift-invariant spaces. Constr. Approx., 8:427-462.
9. M. D. BUHMANN (1993): On quasi-interpolation with radial basis functions. J. Approx. Theory, 72: 103-130.
10. p-Approximation orders with scattered centres.
11. W. DAHMEN, C. A. MICCHELLI (1984): On the approximation order from certain multivariate spline spaces. J. Austral. Math. Soc. Ser. B, 26:233-246.
12. I. DAUBECHIES (1992): Ten lectures on wavelets. Philadelphia, PA: Society for Industrial and Applied Mathematics.
13. N. DYN (1991): Analysis of uniform binary subdivision schemes for curve design. Constr. Approx., 7:127-147.
14. N. DYN, A. RON (1990): Local approximation by certain spaces of multivariate exponential-polynomials, approximation order of exponential box splines and related interpolation problems. Trans. Amer. Math. Soc., 319:381-404.
15. I. M. GELFAND, G. E. SHILOV (1964): Generalized Functions, vol. 1. New York: Academic Press.
16. E. J. HALTON, W. A. LIGHT (1993): On local and controlled approximation order. J. Approx. Theory, 72:268-277.
17. R.-Q. JIA (1993): The Toeplitz Theorem and its Applications to Approximation Theory and Linear PDE's. Manuscript.
18. R.-Q. JIA, J. LEI (1993): Approximation by multi-integer translates of functions having global support. J. Approx. Theory, 72:2-23.
19. Y. KATZNESLON (1968): An introduction to Harmonic Analysis. New York: Wiley.
20. G. C. KYRIAZIS (to appear): Approximation from shift-invariant spaces. Constr. Approx.
21. R. LARSEN (1969): The Multiplier Problem. New York: Springer-Verlag.
22. J. LEI, R.-Q. JIA (1991): Approximation by piecewise exponentials. SIAM J. Math. Anal., 22: 1776-1789.
23. W. A. LIGHT, E. W. CHENEY (1992): Quasi-interpolation with translates of a function having non-compact support. Constr. Approx., 8:35-48.
24. A. RON (1991): A characterization of the approximation order of multivariate spline spaces. Studia Math., 98:73-90.
25. 2-approximation orders of principal shift-invariant spaces generated by a radial basis function. In: Numerical Methods of Approximation Theory (D. Braess, L. L. Schumaker, eds.), vol. 9, pp. 245-268.
26. A. RON (1993): Approximation orders of and approximation maps from local principal shift-invariant spaces. CMS TSR #92-2. University of Wisconsin-Madison, May.
27. G. STRANG, G. Fix (1973): A Fourier analysis of the finite element variational method. In: Constructive Aspects of Functional Analysis (G. Geymonat, ed.). C.I.M.E., pp. 793-840.