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On the block GMRES method with deflated restarting |
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| Authors: | Yiqin Lin Qinghua Wu |
| Institution: | a Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Yongzhou 425100, PR China b School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, PR China c Department of Mathematics, East China University of Science and Technology, Shanghai 200237, PR China |
| Abstract: | In this paper, we consider the block-GMRES method with deflated restarting for solving nonsymmetric linear systems with multiple right-hand sides. We modify slightly the restarted block-GMRES method with deflation of eigenvalues proposed by Morgan to obtain a new one. It is shown that the modified method is mathematically equivalent to the Morgan’s original method. However, the error analysis shows the modified version minimizes the numerical errors during a restart and therefore is better suited if the linear systems have to be solved with high precision. Numerical experiments report the effectiveness of the modified method. |
| Keywords: | Linear system Iterative method Block GMRES Deflation Accuracy Multiple right-hand sides |
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