Multivariate Regression with Emphasis on Multivariate Spline Methods

摘要

The notion of vertex splines is introduced to generalize the univariate spline theory with arbitrary knot sequence to higher dimensions. These are in fact Hermite elements and to facilitate the construction process, the notion of super splines is also introduced. The advantages include efficiency in computing a locally supported basis, guaranteeing the full order of approximation, and various applications to finite element methods, computer-aided geometric design, data analysis, etc. In general, computational schemes are studied and constructed, and interpolation as well as quasi-interpolation problems are solved. Shape-preserved approximation and interpolation by bivariate splines is also studied. Development of general multivariate spline theory including the dimension and basis problems is also a portion of this subject. On the other hand, applications to engineering problems are included in our study. Keywords: Digital signal processing. (kr)