On the smoothness of best l2 approximants from nonlinear spline manifolds

Mathematics of Computation

Volumn 31, Issue 137, 1977, Pages 17-23

  Chui, Rv Charles K ^a   Smith, Philip W ^a   Ward, Joseph D ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84966234735     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1977-0422955-7     Document Type: Article

References (8)

1. C. DEBOOR, "On calculating with B-splines," J. Approximation Theory, v. 6, 1972,. 50-62. MR 49 # 3381.
2. D. BRAESS, "Kritische Punkte bei der nichtlinearen Tschebyscheff-Approximation," Math. Z., v. 132, 1973, pp. 327-341. MR 49 # 962.
3. C. K. CHUI, E. R. ROZEMA, P. W. SMITH & J. D. WARD, "Metric curvature, folding, and unique best approximation," SIAM J. Math. Anal., v. 7, 1976,. 436-449.
4. C. K. CHUI & P. W. SMITH, "Unique best nonlinear approximation in Hilbert spaces, " Proc. Amer. Math. Soc, v. 49, 1975,. 66-70. MR 50 # 14020
5. S. KARLIN, Total Positivity, Vol. 1, Stanford Univ. Press, Stanford, Calif., 1968. MR 37 # 5667.
6. E. R. ROZEMA & P. W. SMITH, "Nonlinear approximation in uniformly smooth Banach spaces," Trans. Amer. Math. Soc., v. 188, 1974,. 199-211. MR 48 # 9212
7. L. L. SCHUMAKER, "Uniform approximation by Chebyshev spline functions. II: Free knots," SIAMJ. Numer. Anal., v. 5, 1968,. 647-656. MR 39 # 3204
8. L. L. SCHUMAKER, "On the smoothness of best spline approximations," J. Approximation Theory, v. 2, 1969,. 410-418. MR 41 # 4076