A direction set based algorithm for least squares problems in adaptive signal processing
A fast algorithm has been developed for solving a class of least squares problems arising in adaptive signal processing. The algorithm is based on the Powell and Zangwill direction set method for unconstrained minimization problems and is designed so as to fully take advantage of the special structu...
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| Published in | Linear algebra and its applications Vol. 284; no. 1; pp. 73 - 94 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
15.11.1998
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0024-3795 1873-1856 |
| DOI | 10.1016/S0024-3795(98)10130-1 |
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| Abstract | A fast algorithm has been developed for solving a class of least squares problems arising in adaptive signal processing. The algorithm is based on the Powell and Zangwill direction set method for unconstrained minimization problems and is designed so as to fully take advantage of the special structure of the adaptive least squares (ALS) problems. It is a fast algorithm because it requires only O(
N) multiplications for each system update where
N is the dimension of the problem. The algorithm has been implemented and applied to applications in signal processing. Computer simulation results have shown that the algorithm is stable and converges fast often with a rate which is comparable to that of the known CG and RLS algorithm. The convergence behavior of the algorithm is studied in detail in this paper. The algorithm is shown to converge linearly for adaptive least squares problems in general and its rate of convergence can be faster than linear for some applications. A computational procedure is also designed to generate a set of near conjugate directions as initial directions to accelerate the convergence. |
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| AbstractList | A fast algorithm has been developed for solving a class of least squares problems arising in adaptive signal processing. The algorithm is based on the Powell and Zangwill direction set method for unconstrained minimization problems and is designed so as to fully take advantage of the special structure of the adaptive least squares (ALS) problems. It is a fast algorithm because it requires only O(
N) multiplications for each system update where
N is the dimension of the problem. The algorithm has been implemented and applied to applications in signal processing. Computer simulation results have shown that the algorithm is stable and converges fast often with a rate which is comparable to that of the known CG and RLS algorithm. The convergence behavior of the algorithm is studied in detail in this paper. The algorithm is shown to converge linearly for adaptive least squares problems in general and its rate of convergence can be faster than linear for some applications. A computational procedure is also designed to generate a set of near conjugate directions as initial directions to accelerate the convergence. |
| Author | Chen, Mei-Qin |
| Author_xml | – sequence: 1 givenname: Mei-Qin surname: Chen fullname: Chen, Mei-Qin email: chenm@citadel.edu organization: Department of Mathematics and Computer Science, The Citadel, Charleston, SC 29409, USA |
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| Cites_doi | 10.1109/TASSP.1983.1164224 10.1137/1004089 10.1137/0909051 10.1109/78.136559 10.1109/81.109237 10.1109/78.388864 10.1137/0613030 10.1109/78.91175 10.1093/imamat/15.3.385 10.1137/0917060 10.1080/00207177808922343 10.1002/(SICI)1099-1506(199601/02)3:1<45::AID-NLA70>3.0.CO;2-T 10.1093/comjnl/10.3.293 10.1093/comjnl/7.2.155 |
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| Copyright | 1998 |
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| Keywords | Adaptive least squares problems Direction set methods |
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| SubjectTerms | Adaptive least squares problems Direction set methods |
| Title | A direction set based algorithm for least squares problems in adaptive signal processing |
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