| D-F-P方法的超线性收敛 |
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| 引用本文： | 姜子文,魏焕彩.D-F-P方法的超线性收敛[J].山东大学学报(工学版),1993(1). |
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| 作者姓名： | 姜子文 魏焕彩 |
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| 作者单位： | 山东师范大学，山东工业大学基础课教学部 |
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| 摘 要： | Powell在文献1]中证明了D-F-P方法是超线性收敛的,Dennis等人在文献2]也给出了同样的结果,但是证明方法不同。本文指出文献2]中的定理3.5有误,证明过程有误,而后给出一个新定理,并用它对于对称正定或负定阵F′(x~*),Dennis等人的结论给出正确的证明。
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| 关 键 词： | 非线性方程 正定矩阵 奇异性 |
SUPERLINEAR CONVERGENCE OF THE D-F-P METHOD |
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| Jiang Ziwen et al.SUPERLINEAR CONVERGENCE OF THE D-F-P METHOD[J].Journal of Shandong University of Technology,1993(1). |
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| Authors: | Jiang Ziwen |
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| Affiliation: | Shandong Normal University |
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| Abstract: | The D-F-P method was proved to be superlinear convergence in reference 1]by Powell. Same result was given in reference 2] by Dennis and More' but the methods used were different between reference 1] and 2]. It is point out that theorem 3.5 in reference 2] and proof given according to above theorem are wrong. A new theorem (theorem 2) and a correct proof for result in reference 2] and a proof for symmetric, positive or negatine definite F'(X~*) are given. |
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| Keywords: | Non-linear equations Positive definite matrices Singularity |
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