Univariate and bivariate orthonormal splines and cardinal splines on compact supports. (English) Zbl 1097.65025

Orthonormal polynomial splines of different smoothness are created. Among the various application to be considered, numerical quadrature is a particularly important one. For this purpose, also splines with (small) compact support are derived. The splines are not only one-dimensional, but also two-dimensional.


65D07 Numerical computation using splines
65D32 Numerical quadrature and cubature formulas
41A15 Spline approximation
41A55 Approximate quadratures
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[1] Chui, C. K., Multivariate Splines, CBMS, vol. 54 (1988), SIAM: SIAM Philadelphia
[3] Liu, X., Bivariate cardinal spline functions for digital signal processing, (Kopotum, K.; Lyche, T.; Neamtu, M., Trends in Approximation Theory (2001), Vanderbilt University Press: Vanderbilt University Press Vanderbilt) · Zbl 1112.94308
[4] Schoenberg, I. J., Contributions to the problem of approximation of equidistance data by analytic functions, Quart. Appl. Math., 4, 45-99 (1946), and 112-141
[5] Schoenberg, I. J., Cardinal Spline Interpolation, CBMS, vol. 12 (1973), SIAM: SIAM Philadelphia · Zbl 0264.41003
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