Adaptive Cross Approximation of Multivariate Functions

In this article we present and analyze a new scheme for the approximation of multivariate functions (d=3,4) by sums of products of univariate functions. The method is based on the Adaptive Cross Approximation (ACA) initially designed for the approximation of bivariate functions. To demonstrate the linear complexity of the schemes, we apply it to large-scale multidimensional arrays generated by the evaluation of functions.