Unicity of best mean approximation by second order splines with variable knots

Mathematics of Computation

Volumn 32, Issue 144, 1978, Pages 1131-1143

  Barrow, D L ^a   Chui, C K ^a   Smith, P W ^a   Ward, J D ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84966238161     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1978-0481754-1     Document Type: Article

References (9)

1. D. L. Barrow, C. K. Chui, P. W. Smith and J. D. Ward, "Unicity of best L2 approximation by second-order splines with variable knots," Bull Amer. Math. Soc., v. 83, 1977, pp. 1049-1050.
2. C. DeBOOR, "Splines as linear combinations of B-splines. A survey," in Approximation Theory. Ii (G. G. Lorentz, C. K. Chui, L. L. Schumaker, Eds.), Academic Press, New York, 1976, pp. 1-47.
3. C. DeBOOR, "On the approximation by y polynomials," in Approximation with Special Emphasis on Spline Functions (I. J. Schoenberg, Ed.), Academic Press, New York, 1969, pp. 157-183.
4. D. Braess, "On the nonuniqueness of monosplines with least Z^-norm," J. Approximation Theory, v. 12, 1974, pp. 91-93.
5. C. K. Chui, P. W. Smith and J. D. Ward, "On the smoothness of best L2 approxi-mants from nonlinear spline manifolds," Math. Comp., v. 37, 1977, pp. 17-23.
6. S. Karlin, C. A. Micchelli, A. Pinkus and I. J. Schoenberg, Studies in Spline Functions and Approximation Theory, Academic Press, New York, 1976.
7. G. Meinardus, Approximation of Functions: Theory and Numerical Methods, Translated by L. L. Schumaker, Springer-Verlag, New York, 1967.
8. J. T. Schwartz, Nonlinear Functional Analysis, Courant Inst, of Math. Sci., New York, 1963.
9. P. W. Smith, "On the smoothness of local best L^ spline approximations," in Approximation Theory, 2 (G. G. Lorentz, C. K. Chui, L. L. Schumaker, Eds.), Academic Press, New York, 1976, pp. 563-566.