| MODIFIED NEWTON＇S ALGORITHM FOR COMPUTING THE GROUP INVERSES OF SINGULAR TOEPLITZ MATRICES |
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| 作者姓名： | Jian-feng Cai Michael K. Ng Yi-min Wei |
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| 作者单位： | [1]Department of Mathematics, The Chinese University of Hong Kong, Hong Kong [2]Department of Mathematics, Hong Kong Baptist University, Hong Kong [3]School of Mathematical Sciences, Fudan University, Shanghai 200433, China ~ Key Laboratory of Mathematics for Nonlinear Sciences （Fudan University）, Ministry of Education |
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| 基金项目： | Research supported in part by the National Natural Science Foundation of China under grant 10471027 and Shanghai Education Committee, RGC 7046/03P, 7035/04P, 7045/05P and HKBU FRGs.The authors would like to thank the referees for their useful suggestions. |
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| 摘 要： | Newton＇s iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton＇s iteration can be done efficiently. We show that the convergence of the modified Newton iteration is still very fast. Numerical results are presented to demonstrate the fast convergence of the proposed method.
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| 关 键 词： | 牛顿迭代 群逆转 Toeplitz矩阵 位移秩 |
| 收稿时间： | 2005-01-12 |
| 修稿时间： | 2005-01-122006-03-20 |
Modified Newton's Algorithm for Computing the Group Inverses of Singular Toeplitz Matrices |
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| Jian-feng Cai Michael K. Ng Yi-min Wei.Modified Newton's Algorithm for Computing the Group Inverses of Singular Toeplitz Matrices[J].Journal of Computational Mathematics,2006,24(5):647-656. |
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| Authors: | Jian-feng Cai Michael K Ng & Yi-min Wei |
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| Abstract: | Newton's iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton's iteration can be done efficiently. We show that the convergence of the modified Newton iteration is still very fast. Numerical results are presented to demonstrate the fast convergence of the proposed method. |
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| Keywords: | Newton's iteration Group inverse Toeplitz matrix Displacement rank |
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