| MODIFIED BERNOULLI ITERATION METHODS FOR QUADRATIC MATRIX EQUATION |
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| 作者姓名： | Zhong-Zhi Bai Yong-Hua Gao |
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| 作者单位： | LSEC,ICMSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China |
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| 基金项目： | Supported by The Special Funds For Major State Basic Research Projects （No. G1999032803）, The China NNSF 0utstanding Young Scientist Foundation （No. 10525102） The National Natural Science Foundation （No. 10471146）, and The National Basic Research Program （No. 2005CB321702）, P.R. China. |
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| 摘 要： | We construct a modified Bernoulli iteration method for solving the quadratic matrix equation AX^2 ＋ BX ＋ C = 0, where A, B and C are square matrices. This method is motivated from the Gauss-Seidel iteration for solving linear systems and the ShermanMorrison-Woodbury formula for updating matrices. Under suitable conditions, we prove the local linear convergence of the new method. An algorithm is presented to find the solution of the quadratic matrix equation and some numerical results are given to show the feasibility and the effectiveness of the algorithm. In addition, we also describe and analyze the block version of the modified Bernoulli iteration method.
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| 关 键 词： | 二次方程式 矩阵 特征值 伯努利 牛顿 局部收敛 |
| 修稿时间： | 2005-12-15 |
MODIFIED BERNOULLI ITERATION METHODS FOR QUADRATIC MATRIX EQUATION |
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| Zhong-Zhi Bai Yong-Hua Gao.MODIFIED BERNOULLI ITERATION METHODS FOR QUADRATIC MATRIX EQUATION[J].Journal of Computational Mathematics,2007,25(5):498-511. |
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