Liu, Xiaoyan Univariate and bivariate orthonormal splines and cardinal splines on compact supports. (English) Zbl 1097.65025 J. Comput. Appl. Math. 195, No. 1-2, 93-105 (2006). 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. Reviewer: Martin D. Buhmann (Gießen) Cited in 2 Documents MSC: 65D07 Numerical computation using splines 65D32 Numerical quadrature and cubature formulas 41A15 Spline approximation 41A55 Approximate quadratures Keywords:cardinal splines; orthonormal polynomial splines; numerical quadrature PDFBibTeX XMLCite \textit{X. Liu}, J. Comput. Appl. Math. 195, No. 1--2, 93--105 (2006; Zbl 1097.65025) Full Text: DOI References: [1] Chui, C. K., Multivariate Splines, CBMS, vol. 54 (1988), SIAM: SIAM Philadelphia [2] C. de Boor, A Practical Guide to Splines, second ed., Applied Mathematical Science, vol. 27, Springer, Berlin, 2001.; C. de Boor, A Practical Guide to Splines, second ed., Applied Mathematical Science, vol. 27, Springer, Berlin, 2001. · Zbl 0987.65015 [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.