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计算矩阵函数双线性形式的Krylov子空间算法的误差分析

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贾仲孝, 孙晓琳
清华大学数学科学系, 北京 100084
收稿日期:2018-10-05出版日期:2020-02-15发布日期:2020-02-15


基金资助:国家自然科学基金资助(项目编号11771249).


THE ERROR ANALYSIS OF THE KRYLOV SUBSPACE METHODS FOR COMPUTING THE BILINEAR FORM OF MATRIX FUNCTIONS

Jia Zhongxiao, Sun Xiaolin
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Received:2018-10-05Online:2020-02-15Published:2020-02-15







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矩阵函数的双线性形式uTfAv出现在很多应用问题中,其中uv ∈ RnA ∈ Rn×nfz)为给定的解析函数.开发其有效可靠的数值算法一直是近年来学术界所关注的问题,其中关于其数值算法的停机准则多种多样,但欠缺理论支持,可靠性存疑.本文将对矩阵函数的双线性形式uTfAv的数值算法和后验误差估计进行研究,给出其基于Krylov子空间算法的误差分析,导出相应的误差展开式,证明误差展开式的首项是一个可靠的后验误差估计,据此可以为算法设计出可靠的停机准则.
MR(2010)主题分类:
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