Document Zbl 0251.41004

Bivariate spline functions and the approximation of linear functionals. (English) Zbl 0251.41004

Numer. Math. 21, 138-160 (1973).

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MSC:

41A15	Spline approximation
41A50	Best approximation, Chebyshev systems
41A45	Approximation by arbitrary linear expressions

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References:

[1]	Ahlberg, J. H., Nilson, E. N.: The approximation of linear functionals. SIAM J. Numer. Anal.3, 173-182 (1966) · Zbl 0147.05102 · doi:10.1137/0703013
[2]	Ahlberg, J. H., Nilson, E. N., Walsh, J. L.: The theory of splines and their applications. New York: Academic Press 1967 · Zbl 0158.15901
[3]	Davis, P. J.: Interpolation and approximation. New York: Blaisdell 1963 · Zbl 0111.06003
[4]	Boor, C. de: Bicubic spline interpolation. J. Math. and Phys.41, 212-218 (1962) · Zbl 0108.27103
[5]	Boor, C. de, Lynch, R. E.: On splines and their minimum properties. J. Math. Mech.15, 953-969 (1966) · Zbl 0185.20501
[6]	Golomb, M., Weinberger, H. F.: Optimal approximation and error bounds. In: On numerical approximation. R. E. Langer (Ed.), p. 117-190. Madison, Wisc.: University of Wisconsin Press 1959 · Zbl 0092.05802
[7]	Mansfield, L. E.: On the optimal approximation of linear functionals in spaces of bivariate functions. SIAM J. Numer. Anal.8, 115-126 (1971) · Zbl 0219.65024 · doi:10.1137/0708015
[8]	Mansfield, L. E.: Optimal approximations and error bounds in spaces of bivariate functions. J. Approx. Theory5, 77-96 (1972) · Zbl 0247.41012 · doi:10.1016/0021-9045(72)90031-7
[9]	Ritter, D.: Two dimensional spline functions and best approximation of linear functionals. J. Approx. Theory3, 352-368 (1970) · Zbl 0203.37001 · doi:10.1016/0021-9045(70)90040-7
[10]	Sard, A.: Linear approximation. Math. Surveys No.9, American Mathematical Society, Providence, Rhode Island (1963) · Zbl 0115.05403
[11]	Schoenberg, I. J.: Spline interpolation and best quadrature formulae. Bull. Amer. Math. Soc.70, 143-148 (1964) · Zbl 0136.36202 · doi:10.1090/S0002-9904-1964-11054-5
[12]	Schoenberg, I. J.: On Monosplines of least deviation and best quadrature formulae I. SIAM J. Numer. Anal.2, 144-170 (1965), Ibid.3, 321-328 (1966) · Zbl 0136.36203
[13]	Schoenberg, I. J.: On the Ahlberg-Nilson extension of spline interpolation: theg-spline and their optimal properties. J. of Math. Anal. and Appl.21, 207-231 (1968) · Zbl 0159.08401 · doi:10.1016/0022-247X(68)90252-7
[14]	Secrest, D.: Best approximate integration formulas and best error bounds. Math. comp.19, 79-83 (1965) · Zbl 0134.13606
[15]	Secrest, D.: Numerical integration of arbitrarily spaced data and estimation of errors. SIAM J. Numer. Anal.2, 52-58 (1965) · Zbl 0135.38601
[16]	Secrest, D.: Error bounds for interpolation and differentiation by the use of spline functions. SIAM J. Numer. Anal.2, 440-447 (1965) · Zbl 0143.38804

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