| A MODIFIED INVERSE ITERATION FOR A LARGE SPARSE SPD GENERALIZED EIGENPROBLEM |
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| 引用本文： | 於崇华
,O.Axelsson.A MODIFIED INVERSE ITERATION FOR A LARGE SPARSE SPD GENERALIZED EIGENPROBLEM[J].高等学校计算数学学报(英文版),1999(2). |
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| 作者姓名： | 於崇华 O.Axelsson |
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| 作者单位： | Yu Chonghua O. AxelssonDepartment of Mathematics，Fudan University，Shanghai 200433，PRC.Faculty of Mathematics and Informatics，University of Nijmegen 6525，ED Nijmegen，The Netherlands. |
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| 摘 要： | In this paper, an algorithm based on a shifted inverse power iteration for computing generalized eigenvalues with corresponding eigenvectors of a large scale sparse symmetric positive definite matrix pencil is presented. It converges globally with a cubic asymptotic convergence rate, preserves sparsity of the original matrices and is fully parallelizable. The algebraic multilevel itera-tion method (AMLI) is used to improve the efficiency when symmetric positive definite linear equa-tions need to be solved.
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A MODIFIED INVERSE ITERATION FOR A LARGE SPARSE SPD GENERALIZED EIGENPROBLEM |
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| Yu Chonghua O. Axelsson.A MODIFIED INVERSE ITERATION FOR A LARGE SPARSE SPD GENERALIZED EIGENPROBLEM[J].Numerical Mathematics A Journal of Chinese Universities English Series,1999(2). |
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| Authors: | Yu Chonghua O Axelsson |
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| Institution: | Yu Chonghua O. AxelssonDepartment of Mathematics,Fudan University,Shanghai 200433,PRC.Faculty of Mathematics and Informatics,University of Nijmegen 6525,ED Nijmegen,The Netherlands. |
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| Abstract: | In this paper, an algorithm based on a shifted inverse power iteration for computing generalized eigenvalues with corresponding eigenvectors of a large scale sparse symmetric positive definite matrix pencil is presented. It converges globally with a cubic asymptotic convergence rate, preserves sparsity of the original matrices and is fully parallelizable. The algebraic multilevel iteration method (AMLI) is used to improve the efficiency when symmetric positive definite linear equations need to be solved. |
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| Keywords: | Generalized eigenvalue problem shifted inverse power iteration convergence algebraic multilevel iteration method |
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