The Adaptive Cross Approximation (ACA) algorithm is a well-established tool in numerical modelling, used for fast and accurate compression of interaction matrices. The tradeoff between efficiency and memory requirements on the one hand, and accuracy on the other, is governed by a precision threshold and an accompanying approximate convergence criterion. It has long been known that this convergence criterion is
sometimes very unreliable, yet despite the widespread success of the ACA, no viable al...
The Adaptive Cross Approximation (ACA) algorithm is a well-established tool in numerical modelling, used for fast and accurate compression of interaction matrices. The tradeoff between efficiency and memory requirements on the one hand, and accuracy on the other, is governed by a precision threshold and an accompanying approximate convergence criterion. It has long been known that this convergence criterion is
sometimes very unreliable, yet despite the widespread success of the ACA, no viable alternative has been proposed to date.
In this contribution we shall illustrate the extent of the risk that this unreliability entails with an example involving a small and simple geometry. The features that influence the error in the criterion and the resulting error in the numerical solution, as well as the fact that it is statistical in nature although this is somewhat obscured in the formulation of the algorithm, will be discussed.
Subsequently a new convergence criterion will be presented and shown to largely eliminate the above mentioned problem without compromising the overall computational efficiency of the ACA algorithm.
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