| 一类基于广义逆的矩阵连分式收敛性 |
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| 引用本文： | 赵欢喜,朱功勤.一类基于广义逆的矩阵连分式收敛性[J].中国科学技术大学学报,2002,32(4):412-416. |
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| 作者姓名： | 赵欢喜 朱功勤 |
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| 作者单位： | 1. 中国科学技术大学数学系,安徽合肥,230026:中南大学数学院,湖南长沙,410083
2. 合肥工业大学理学院,安徽合肥,230009 |
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| 基金项目： | 国家自然科学基金资助项目 (10 1710 2 6 ) |
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| 摘 要： | 讨论了一类基于Samelson逆的正矩阵值连分式的收敛性，建立了一种所谓的矩阵连分式的向后三项递推关系式，并利用此关系式研究了这种矩阵值连分式的渐近方式的性质以及给出了收敛的一些充分条件，它们中的一些结果甚至是数量连分式的相应结果的准确推广及改进。
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| 关 键 词： | 矩阵连分式 收敛性 矩阵值连分式 收敛定理 矩阵广义逆 渐近方式 Samelson逆 |
| 文章编号： | 0253-2778(2002)04-0412-05 |
Convergence of a Class of Matrix Continued Fractions Based on the Generalized Inverse |
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| ZHAO Huan xi ,ZHU Gong qin.Convergence of a Class of Matrix Continued Fractions Based on the Generalized Inverse[J].Journal of University of Science and Technology of China,2002,32(4):412-416. |
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| Authors: | ZHAO Huan xi ZHU Gong qin |
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| Institution: | ZHAO Huan xi 1,2,ZHU Gong qin 3 |
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| Abstract: | We consider a class of matrix valued continued fractions with positive elements, which are defined by the generalized(Samelson) inverse. We begin to give a so called backward three term recurrence algorithm for matrix valued continued fractions. By means of this relation, the properties of the convergents of matrix valued continued fractions are discussed. A few sufficient conditions of the convergence are obtained, and some of them are exact generalzation or improvement of the scalar results. |
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| Keywords: | matrix continued fractions convergence theorem generalized matrix inverse |
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