| Hilbert空间中算子求逆条件数在误差分析中的最小性 |
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| 引用本文： | 陈果良.Hilbert空间中算子求逆条件数在误差分析中的最小性[J].上海师范大学学报(自然科学版),1987(1). |
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| 作者姓名： | 陈果良 |
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| 作者单位： | 华东师范大学数学系 |
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| 摘 要： | 本文利用Hilbert空间中可逆算子的极分解定理,证明了线性有界算子A的求逆条件数K(A)=||A||||A~(-1)||在求算子扰动逆(A E)~(-1)时的相对误差界中的极小性质.指出算子求逆条件数在误差估计中为仅与算子A有关的最佳常数值。推广了文献4]中的全部结果。
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| 关 键 词： | 求逆条件数K(A) 误差估计 最佳常数值 病态 |
Minimalness in the Error Estimation Condition Number with Respect to Inversion of Operator in Hilbert Space |
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| CHENGUOLIANG.Minimalness in the Error Estimation Condition Number with Respect to Inversion of Operator in Hilbert Space[J].Journal of Shanghai Normal University(Natural Sciences),1987(1). |
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| Authors: | CHENGUOLIANG |
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| Institution: | Department of Mathematics |
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| Abstract: | The condition number K (A) with respect to inversion of linear bound operator A in Hilbert Space is proved to be an important role in the error estimation of numerical solution for linear equation system and matrix inversion.
It is pointed that the condition number K (A) is an optimal value, only depends on operator A, and the smaller the better. Otherwise, the problem will approach illcondition. |
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| Keywords: | the condition number K(A) with respect to inversion error estimation the optimal value ill-condition |
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