Adaptive low-rank approximation of collocation matrices. (English) Zbl 1068.41052

In this paper there is dealt with the solution of integral equations using collocation methods with almost linear complexity. There are used fast multipole, panel clustering and \(H\)-matrix methods which gain their efficiency from approximating the kernel function. The proposed \(H\)-matrix algorithm is purely algebraic. A new algorithm for matrix partitioning significantly reducing the number of blocks generated is presented.


41A63 Multidimensional problems
41A80 Remainders in approximation formulas
65D05 Numerical interpolation
65D15 Algorithms for approximation of functions
65F05 Direct numerical methods for linear systems and matrix inversion
65F30 Other matrix algorithms (MSC2010)
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