| 基于Samelson逆的向量值连分式的收敛准则 |
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| 引用本文： | 赵欢喜,肖萍. 基于Samelson逆的向量值连分式的收敛准则[J]. 高等学校计算数学学报, 2004, 26(1): 18-24 |
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| 作者姓名： | 赵欢喜 肖萍 |
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| 作者单位： | 中南大学数学院应用数学与应用软件系,长沙,410083;中国科技大学数学系,合肥,230026;中南大学数学院应用数学与应用软件系,长沙,410083 |
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| 摘 要： | The aim of this work is to give some criteria on the convergence of vector valued continued fractions defined by Samelson inverse. We give a new approach to prove the convergence theory of continued fractions. First, by means of the modified classical backward recurrence relation, we obtain a formula between the m-th and n-th convergence of vector valued continued fractions. Second, using this formula, we give necessary and sufficient conditions for the convergence of vector valued continued fractions.
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| 关 键 词： | Samelson逆 向量值连分式 收敛准则 向后递推算法 |
CONVERGENCE CRITERIA FOR VECTOR VALUED CONTINUED FRACTIONS BASED ON SAMELSON INVERSE |
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| Zhao Huanxi. CONVERGENCE CRITERIA FOR VECTOR VALUED CONTINUED FRACTIONS BASED ON SAMELSON INVERSE[J]. Numerical Mathematics A Journal of Chinese Universities, 2004, 26(1): 18-24 |
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| Authors: | Zhao Huanxi |
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| Abstract: | The aim of this work is to give some criteria on the convergence of vector valued continued fractions defined by Samelson inverse. We give a new approach to prove the convergence theory of continued fractions. First, by means of the modified classical backward recurrence relation, we obtain a formula between the m-th and n-th convergence of vector valued continued fractions. Second, using this formula, we give necessary and sufficient conditions for the convergence of vector valued continued fractions. |
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| Keywords: | continued fractions backward recurrence relation convergence for-mula convergence criteria. |
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