Multivariate polynomial spline spaces
Spaces of polynomial splines are considered in \(p (\geq 2)\) variables, defined on rectangular grids. This paper provides a natural generalization of the bivariate case as studied by \textit{C. K. Chui} and \textit{R. H. Wang} [J. Math. Anal. Appl. 94, 197-221 (1983, Zbl 0526.41027)] to the \(p\)-variate case. The smoothness conditions imposed can be homogeneous, semi-homogeneous or nonhomogeneous [see \textit{C. K. Chui} and \textit{R. H. Wang}, Math. Comput. 41, 131-142 (1983, Zbl 0542.41008)]. Bases, and hence dimensions, for the polynomial spline spaces for these different smoothness cases are explicitly constructed. The bases can be written in terms of polynomials and truncated powers and products of these functions.
scientific article; zbMATH DE number 1439635
scientific article