Scattered data approximation on the bisphere and application to texture analysis
The focus of the paper is to obtain an optimal approximation and interpolation on the bisphere from scattered data. First, the authors collect the basic material on the harmonic analysis on the bisphere (Section 2). Next, they explain the basics for computation on the bisphere (Section 3). The main results of the paper are contained in Section 4, where the authors provide the approximation and interpolation of scattered data in their setting: the Marcienkiewicz-Zygmund inequality (Theorem 6), the estimate of the condition number (Corollary 7), an optimal interpolation problem (Theorem 11), an estimate of the condition number for the normal equation (Corollary 12). Section 5 contains some applications, concerning a texture analysis.
bisphere Marcienkiewicz-Zygmund inequality
scientific article; zbMATH DE number 5809625
scientific article