A Sparse Matrix Arithmetic Based on \Cal H-Matrices. Part I: Introduction to {\Cal H}-Matrices |
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Authors: | W Hackbusch |
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Affiliation: | (1) Max Planck Institut Mathematik in den Naturwissenschaften Insel str. 22--26, D-04103 Leipzig, Germany, e-mail: wh@mis.mpg.de , DE |
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Abstract: | A class of matrices (-matrices) is introduced which have the following properties. (i) They are sparse in the sense that only few data are needed
for their representation. (ii) The matrix-vector multiplication is of almost linear complexity. (iii) In general, sums and
products of these matrices are no longer in the same set, but their truncations to the -matrix format are again of almost linear complexity. (iv) The same statement holds for the inverse of an -matrix.
This paper is the first of a series and is devoted to the first introduction of the -matrix concept. Two concret formats are described. The first one is the simplest possible. Nevertheless, it allows the exact
inversion of tridiagonal matrices. The second one is able to approximate discrete integral operators.
Received: July 30, 1998; revised December 28, 1998 |
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Keywords: | AMS Subject Classifications:65F05 65F30 65F50 |
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