On the uniqueness of best approximation by piecewise polynomials with variable breakpoints
Math. Comp. 39 (1982), 571-585
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Abstract: In this paper a sufficient condition for the uniqueness of best approximation by piecewise polynomials of order k with variable breakpoints is generalized from that of order 2. Other extensions included here are nonuniqueness and eventual uniqueness results.
L. Barrow, C.
K. Chui, P.
W. Smith, and J.
D. Ward, Unicity of best mean approximation by
second order splines with variable knots, Math.
Comp. 32 (1978), no. 144, 1131–1143. MR 0481754
(58 #1853), http://dx.doi.org/10.1090/S0025-5718-1978-0481754-1
G. Burchard and D.
F. Hale, Piecewise polynomial approximation on optimal meshes,
J. Approximation Theory 14 (1975), no. 2,
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J. Davis, Interpolation and approximation, Blaisdell
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M. Ortega, Numerical analysis. A second course, Academic
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T. Schwartz, Nonlinear functional analysis, Gordon and Breach
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- D. L. Barrow, C. K. Chui, P. W. Smith & J. D. Ward, "Unicity of best mean approximation by second order splines with variable knots," Math. Comp., v. 32, 1978, pp. 1131-1143. MR 0481754 (58:1853)
- H. G. Burchard & D. F. Hale, "Piecewise polynomial approximation on optimal meshes," J. Approx. Theory, v. 14, 1975, pp. 128-147. MR 0374761 (51:10957)
- P. J. Davis, Interpolation and Approximation, Blaisdell, Waltham, Mass., 1963. MR 0157156 (28:393)
- J. M. Ortega, Numerical Analysis, Academic Press, New York, 1972. MR 0403154 (53:6967)
- W. Rudin, Functional Analysis, McGraw-Hill, New York, 1973. MR 0365062 (51:1315)
- J. T. Schwartz, Nonlinear Functional Analysis, Gordon and Breach, New York, 1969. MR 0433481 (55:6457)
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