Integration and approximation of multivariate functions: average case complexity with isotropic Wiener measure
Abstract
We study the average case complexity of multivariate integration and L2 function approximation for the class F=C([0,1]d) of continuous functions of d variables. The class F is endowed with the isotropic Wiener measure (Brownian motion in Levy's sense). Furthermore, for both problems, only function values are used as data.
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