On the QR Decomposition of H-Matrices
The hierarchical (<i>H-</i>) matrix format allows storing a variety of dense matrices from certain applications in a special data-sparse way with linear-polylogarithmic complexity. Many operations from linear algebra like matrix-matrix and matrix-vector products, matrix inversion and L...
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| Language: | English |
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Technische Universität Chemnitz
2009
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| Online Access: | http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200901420 https://monarch.qucosa.de/id/qucosa%3A19190 https://monarch.qucosa.de/api/qucosa%3A19190/attachment/ATT-0/ https://monarch.qucosa.de/api/qucosa%3A19190/attachment/ATT-1/ |
| Summary: | The hierarchical (<i>H-</i>) matrix format allows storing a variety of dense matrices from certain applications in a special data-sparse way with linear-polylogarithmic complexity. Many operations from linear algebra like matrix-matrix and matrix-vector products, matrix inversion and LU decomposition can be implemented efficiently using the <i>H</i>-matrix format. Due to its importance in solving many problems in numerical linear algebra like least-squares problems, it is also desirable to have an efficient QR decomposition of <i>H</i>-matrices. In the past, two different approaches for this task have been suggested. We will review the resulting methods and suggest a new algorithm to compute the QR decomposition of an <i>H</i>-matrix. Like other <i>H</i>-arithmetic operations the <i>H</i>QR decomposition is of linear-polylogarithmic complexity. We will compare our new algorithm with the older ones by using two series of test examples and discuss benefits and drawbacks of the new approach. |
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