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This paper presents a novel {\em Interpolated Factored Green Function} method(IFGF) for the accelerated evaluation of the integral operators in scatteringtheory and other areas. Like existing acceleration methods in these fields, theIFGF algorithm evaluates the action of Green function-based integral operatorsat a cost of $\mathcal{O}(N\log N)$ operations for an $N$-point surface mesh.The IFGF strategy, which leads to an extremely simple algorithm, capitalizes onslow variations inherent in a certain Green function {\em analytic factor},which is analytic up to and including infinity, and which therefore allows foraccelerated evaluation of fields produced by groups of sources on the basis ofa recursive application of classical interpolation methods. Unlike otherapproaches, the IFGF method does not utilize the Fast Fourier Transform (FFT),and is thus better suited than other methods for efficient parallelization indistributed-memory computer systems. Only a serial implementation of thealgorithm is considered in this paper, however, whose efficiency in terms ofmemory and speed is illustrated by means of a variety of numerical experiments-- including a 43 min., single-core operator evaluation (on 10 GB of peakmemory), with a relative error of $1.5\times 10^{-2}$, for a problem ofacoustic size of 512$\lambda$.

"Interpolated Factored Green Function" Method for accelerated solution of Scattering Problems