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A class of vector-space bases is introduced for the sparse representation of discretizations of integral operators. An operator with a smooth, nonoscillatory kernel possessing a finite number of singularities in each row or column is represented in these bases as a sparse matrix, to high precision. A method is presented that employs these bases for the numerical solution of second-kind integral equations in time bounded by O (n ² n), where n is the number of points in the discretization. Numerical results are given which demonstrate the effectiveness of the approach, and several generalizations and applications of the method are discussed.
Alpert et al. (Fri,) studied this question.
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