A new Nested Cross Approximation
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In this article, we present a new Nested Cross Approximation (NCA), for ℋ^2 matrices with well-separated admissibility condition, i.e., the interaction between neighboring cluster of particles is considered full-rank, while the interaction between well-separated cluster of particles can be efficiently approximated by a low-rank matrix. It differs from the existing NCAs in the technique of choosing pivots, a key part of the approximation. Our technique of choosing pivots is purely algebraic and involves only a single tree traversal. We demonstrate its applicability by developing an Algebraic Fast Multipole Method (AFMM), that uses NCA for the appropriate low-rank approximations. We perform various numerical experiments to illustrate the timing profiles and the accuracy of our method. We also provide a comparison of the proposed NCA with the existing NCAs.
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