MULTISCALE ANALYSIS OF MULTIVARIATE DATA

For many applications, nonuniformly distributed functional data is given which lead to large–scale scattered data problems. We wish to represent the data in terms of a sparse representation with a minimal amount of degrees of freedom. For this, an adaptive scheme which operates in a coarse-to-fine fashion using a multiscale basis is proposed. Specifically, we investigate hierarchical bases using B-splines and spline-(pre)wavelets. At each stage a leastsquares approximation of the data is computed. We take into account different requests arising in large-scale scattered data fitting: we discuss the fast iterative solution of the least square systems, regularization of the data, and the treatment of outliers. A particular application concerns the approximate continuation of harmonic functions, an issue arising in geodesy.