This article deals with the solution of integral equations using collocation methods with almost linear complexity. Methods such as fast multipole, panel clustering and ℋ-matrix methods gain their efficiency from approximating the kernel function. The proposed algorithm which uses the ℋ-matrix format, in contrast, is purely algebraic and relies on a small part of the collocation matrix for its blockwise approximation by low-rank matrices. Furthermore, a new algorithm for matrix partitioning that significantly reduces the number of blocks generated is presented.
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Received August 15, 2002; revised September 20, 2002 Published online: March 6, 2003
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Bebendorf, M., Rjasanow, S. Adaptive Low-Rank Approximation of Collocation Matrices. Computing 70, 1–24 (2003). https://doi.org/10.1007/s00607-002-1469-6
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DOI: https://doi.org/10.1007/s00607-002-1469-6