The block LSMR algorithm for solving linear systems with multiple right-hand sides
Year
: 2015
Abstract: LSMR (Least Squares Minimal Residual) is an iterative method for the solution of the linear system of equations and least-squares problems. This paper presents a block version of the LSMR algorithm for solving linear systems with multiple right-hand sides. The new algorithm is based on the block
bidiagonalization and derived by minimizing the Frobenius norm of the residual matrix of normal equations. In addition, the convergence of the proposed algorithm is discussed. In practice, it is also observed that the Frobenius norm of the residual matrix decreases monotonically. Finally, numerical experiments from real applications are employed to verify the effectiveness of the presented method.
bidiagonalization and derived by minimizing the Frobenius norm of the residual matrix of normal equations. In addition, the convergence of the proposed algorithm is discussed. In practice, it is also observed that the Frobenius norm of the residual matrix decreases monotonically. Finally, numerical experiments from real applications are employed to verify the effectiveness of the presented method.
Keyword(s): LSMR method,Bidiagonalization,Block methods,Iterative methods,Multiple right-hand sides
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The block LSMR algorithm for solving linear systems with multiple right-hand sides
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| contributor author | فائزه توتونیان مشهد | en |
| contributor author | مریم مجرب | en |
| contributor author | Faezeh Toutounian Mashhad | fa |
| contributor author | maryam mojarrab | fa |
| date accessioned | 2020-06-06T13:27:49Z | |
| date available | 2020-06-06T13:27:49Z | |
| date issued | 2015 | |
| identifier uri | https://libsearch.um.ac.ir:443/fum/handle/fum/3355876 | |
| description abstract | LSMR (Least Squares Minimal Residual) is an iterative method for the solution of the linear system of equations and least-squares problems. This paper presents a block version of the LSMR algorithm for solving linear systems with multiple right-hand sides. The new algorithm is based on the block bidiagonalization and derived by minimizing the Frobenius norm of the residual matrix of normal equations. In addition, the convergence of the proposed algorithm is discussed. In practice, it is also observed that the Frobenius norm of the residual matrix decreases monotonically. Finally, numerical experiments from real applications are employed to verify the effectiveness of the presented method. | en |
| language | English | |
| title | The block LSMR algorithm for solving linear systems with multiple right-hand sides | en |
| type | Journal Paper | |
| contenttype | External Fulltext | |
| subject keywords | LSMR method | en |
| subject keywords | Bidiagonalization | en |
| subject keywords | Block methods | en |
| subject keywords | Iterative methods | en |
| subject keywords | Multiple right-hand sides | en |
| journal title | Iranian Journal of Numerical Analysis and Optimization | fa |
| pages | 28-Nov | |
| journal volume | 5 | |
| journal issue | 2 | |
| identifier link | https://profdoc.um.ac.ir/paper-abstract-1054107.html | |
| identifier articleid | 1054107 |