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s00190-011-0490-y.pdf | 412.63 kB | Adobe PDF | 見る/開く |
タイトル: | Parallel Cholesky-based reduction for the weighted integer least squares problem |
著者: | Xu, Peiliang https://orcid.org/0000-0003-1830-8401 (unconfirmed) |
著者名の別形: | 徐, 培亮 |
キーワード: | Global positioning system (GPS) Integer linear model Integer least squares Closest point problem Reduction of quadratic forms LLL reduction Multiple-input–multiple-output |
発行日: | Jan-2012 |
出版者: | Springer-Verlag |
誌名: | Journal of Geodesy |
巻: | 86 |
号: | 1 |
開始ページ: | 35 |
終了ページ: | 52 |
抄録: | The LLL reduction of lattice vectors and its variants have been widely used to solve the weighted integer least squares (ILS) problem, or equivalently, the weighted closest point problem. Instead of reducing lattice vectors, we propose a parallel Cholesky-based reduction method for positive definite quadratic forms. The new reduction method directly works on the positive definite matrix associated with the weighted ILS problem and is shown to satisfy part of the inequalities required by Minkowski’s reduction of positive definite quadratic forms. The complexity of the algorithm can be fixed a priori by limiting the number of iterations. The simulations have clearly shown that the parallel Cholesky-based reduction method is significantly better than the LLL algorithm to reduce the condition number of the positive definite matrix, and as a result, can significantly reduce the searching space for the global optimal, weighted ILS or maximum likelihood estimate. |
著作権等: | The final publication is available at www.springerlink.com This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。 |
URI: | http://hdl.handle.net/2433/152556 |
DOI(出版社版): | 10.1007/s00190-011-0490-y |
出現コレクション: | 学術雑誌掲載論文等 |
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