"A dimension-incremental approximation method for arbitrary bounded orthonormal product bases"
Taubert, FabianWe present a dimension-incremental algorithm for the approximation of high-dimensional, multivariate functions in an arbitrary bounded orthonormal product basis. The goal is a truncation of the basis expansion of the function, where the corresponding index set is unknown. Our method is based on point evaluations of the considered function and adaptively builds a good index set, such that the approximately largest basis coefficients are still included. Throughout the work, there are several minor modifications of the algorithm discussed as well, which may yield additional benefits in some situations. We provide an exemplary proof of a detection guarantee for such an index set under certain assumptions on the sub-methods used within our algorithm, which can be used as a foundation for similar statements in various other situations as well. Some numerical examples in different settings underline the effectiveness and accuracy of our method.