On the uniqueness of best $L_{2}[0, 1]$ approximation by piecewise polynomials with variable breakpoints
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- by Jeff Chow PDF
- Math. Comp. 39 (1982), 571-585 Request permission
Abstract:
In this paper a sufficient condition for the uniqueness of best ${L_2}[0,1]$ 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.References
- D. 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 481754, DOI 10.1090/S0025-5718-1978-0481754-1
- H. G. Burchard and D. F. Hale, Piecewise polynomial approximation on optimal meshes, J. Approximation Theory 14 (1975), no. 2, 128–147. MR 374761, DOI 10.1016/0021-9045(75)90084-2
- Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1963. MR 0157156
- James M. Ortega, Numerical analysis. A second course, Computer Science and Applied Mathematics, Academic Press, New York-London, 1972. MR 0403154
- Walter Rudin, Functional analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. MR 0365062
- J. T. Schwartz, Nonlinear functional analysis, Notes on Mathematics and its Applications, Gordon and Breach Science Publishers, New York-London-Paris, 1969. Notes by H. Fattorini, R. Nirenberg and H. Porta, with an additional chapter by Hermann Karcher. MR 0433481
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Math. Comp. 39 (1982), 571-585
- MSC: Primary 41A15
- DOI: https://doi.org/10.1090/S0025-5718-1982-0669650-9
- MathSciNet review: 669650