Nonexistence of star-supported spline bases

SIAM Journal on Mathematical Analysis

Volumn 31, Issue 2, 2000, Pages 455-465

  Alfeld, Peter ^a   Schumaker, Larry L ^b  

^a UNIVERSITY OF UTAH   (United States)

^b VANDERBILT UNIVERSITY   (United States)

Author keywords

Multivariate splines; Piecewise polynomial functions; Triangulations

Indexed keywords

EID: 0033474148     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141098342349     Document Type: Article

References (14)

1. P. ALFELD AND L.L. SCHUMAKER, The dimension of bivariate spline spaces of smoothness r for degree d ≥ 4r + 1, Constr. Approx., 3 (1987), pp. 189-197.
2. P. ALFELD AND L.L. SCHUMAKER, Minimally supported bases for spaces of bivariate piecewise polynomials of smoothness r and degree d ≥ 4r + 1, Comput. Aided Geom. Design, 4 (1987), pp. 105-123.
3. 1 quartic bivariate splines, SIAM J. Numer. Anal., 24 (1987), pp. 891-911.
4. P. ALFELD AND L.L. SCHUMAKER, On the dimension of bivariate splines spaces of smoothness r and degree d = 3r + 1, Numer. Math., 3 (1990), pp. 651-661.
5. 1-cubics: a counterexample, Proc. Amer. Math. Soc., 87 (1983), pp. 649-655.
6. C. DE BOOR AND R.Q. JIA, A sharp upper bound on the approximation order of smooth bivariate pp functions, J. Approx. Theory, 72 (1993), pp. 24-33.
7. O.K. CHUI, D. HONG, AND R.Q. JIA, Stability of optimal order approximation by bivariate splines over arbitrary triangulations, Trans. Amer. Math. Soc., 347 (1995), pp. 3301-3318.
8. O.K. CHUI AND M.J. LAI, On bivariate vertex splines, in Multivariate Approximation Theory III, Internat. Ser. Numer. Math. 73, W. Schempp and K. Zeller, eds., Birkhäuser-Verlag, Basel, Switzerland, 1985, pp. 84-115.
9. D. HONG, Spaces of bivariate spline functions over triangulation, Approx. Theory Appl., 7 (1991), pp. 56-75.
10. A. IBRAHIM AND L.L. SCHUMAKER, Superspline spaces of smoothness r and degree d ≥ 3r + 2, Constr. Approx., 7 (1991), pp. 401-423.
11. M.J. LAI AND L.L. SCHUMAKER, On the approximation power of bivariate splines, Adv. Comput. Math., 9 (1998), pp. 251-279.
12. L.L. SCHUMAKER, On the dimension of multivariate piecewise polynomials, in Numerical Analysis, D. F. Griffiths and G. A. Watson, eds., Longman Scientific and Technical, Harlow, UK, 1986, pp. 1-23.
13. L.L. SCHUMAKER, Bounds on the dimension of spaces of multivariate piecewise polynomials, Rocky Mountain J. Math., 14 (1984), pp. 251-264.
14. L.L. SCHUMAKER, Dual bases for spline spaces on cells, Comput. Aided Geom. Design, 5 (1988), pp. 277-284.