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We present a fast, adaptive multiresolution algorithm for applying integraloperators with a wide class of radially symmetric kernels in dimensions one,two and three. This algorithm is made efficient by the use of separatedrepresentations of the kernel. We discuss operators of the class$(-\Delta+\mu^{2}I)^{-\alpha}$, where $\mu\geq0$ and $0<\alpha<3/2$, andillustrate the algorithm for the Poisson and Schr\"{o}dinger equations indimension three. The same algorithm may be used for all operators with radiallysymmetric kernels approximated as a weighted sum of Gaussians, making itapplicable across multiple fields by reusing a single implementation.  This fast algorithm provides controllable accuracy at a reasonable cost,comparable to that of the Fast Multipole Method (FMM). It differs from the FMMby the type of approximation used to represent kernels and has an advantage ofbeing easily extendable to higher dimensions.

Fast Adaptive Algorithms in the Non-Standard Form for Multidimensional Problems