Bivariate segment approximation and free knot splines: Research problems 96-4

Constructive Approximation

Volumn 12, Issue 4, 1996, Pages 555-558

  Nurnberger G ^a  

^a UNIVERSITY OF MANNHEIM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040749593     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02437508     Document Type: Article

References (22)

1. C. DE BOOR (1978): A Practical Guide to Splines. New York: Springer-Verlag.
2. D. BRAESS (1986): Nonlinear Approximation Theory. Berlin: Springer-Verlag.
3. C. K. CHUI (1988): Multivariate Splines. Philadelphia: CBMS-SIAM.
4. R A. DEVORE, G. G. LORENTZ (1993): Constructive Approximation. New York: Springer-Verlag.
5. R. S. JOHNSON (1960): On monosplines of least deviation. Trans. Amer. Math. Soc., 96:458-477.
6. H. KAWASAKI (1994): A second-order property of spline functions with one free knot. J. Approx. Theory, 78:293-297.
7. G. MEINARDUS (1967): Approximation of Functions: Theory and Numerical Methods. Berlin: Springer-Verlag.
8. G. MEINARDUS, G. NÜRNBERGER, M. SOMMER, H. STRAUSS (1989): Algorithms for piecewise polynomials and splines with free knots. Math. Comput., 53:235-247.
9. G. MEINARDUS, G. NÜRNBERGER, G. WALZ (to appear): Bivariate segment approximation and splines. Advances in Computational Mathematics.
10. B. MULANSKY (1992): Chebyshev approximation by spline functions with free knots. IMA J. Numer. Anal., 12:95-105.
11. B. MULANSKY (1992): Necessary conditions for local best Chebyshev approximations by splines with free knots. In: Numerical Methods of Approximation Theory (D. Braess, L. L. Schumaker, eds.). ISNM, 105. Basel: Birkäuser, pp. 195-206.
12. G. NÜRNBERGER (1987): Strongly unique spline approximation with free knots. Constr. Approx., 3:31-42.
13. G. NÜRNBERGER (1989): Approximation by Spline Functions. Berlin: Springer-Verlag.
14. G. NÜRNBERGER (1992): The metric projection for free knot splines. J. Approx. Theory, 71:145-153.
15. G. NÜRNBERGER (1994a): Strong unicity in nonlinear approximation and free knot splines. Constr. Approx., 10:285-299.
16. G. NÜRNBERGER (1994b): Approximation by univariate and bivariate splines. In: Second International Colloquium on Numerical Analysis (D. Bainov, V. Covachev, eds.). Utrecht: VSP, pp. 143-153.
17. G. NÜRNBERGER, L. L. SCHUMAKER, M. SOMMER, H. STRAUSS (1989): Uniform approximation by generalized splines with free knots. J. Approx. Theory, 59:150-169.
18. G. NÜRNBERGER, M. SOMMER (1983): A Remez type algorithm for spline functions. Numer. Math., 41:117-146.
19. G. NÜRNBERGER, M. SOMMER, H. STRAUSS (1986): An algorithm for segment approximation. Numer. Math., 48:463-477.
20. M. J. D. POWELL (1981): Approximation Theory and Methods. Cambridge, UK: Cambridge University Press.
21. L. L. SCHUMAKER (1981): Spline Functions: Basic Theory. New York: Wiley-Interscience.
22. M. SOMMER (1992): Segment approximation using linear functionals. In: Numerical Methods of Approximation Theory (D. Braess, L. L. Schumaker, eds.). ISNM, 105. Basel: Birkäuser, pp. 331-346.