• 论文 •

计算矩阵函数双线性形式的Krylov子空间算法的误差分析

1. 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）.

Jia Zhongxiao, Sun Xiaolin. THE ERROR ANALYSIS OF THE KRYLOV SUBSPACE METHODS FOR COMPUTING THE BILINEAR FORM OF MATRIX FUNCTIONS[J]. Mathematica Numerica Sinica, 2020, 42(1): 117-130.

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

Jia Zhongxiao, Sun Xiaolin

1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
• Received:2018-10-05 Online:2020-02-15 Published:2020-02-15

The bilinear form uTf(A)v of matrix functions is of wide interest in many applications, where u, v ∈ Rn, A ∈ Rn×n, f(z) is a given analytic function. In recent years, the efficient and reliable numerical algorithms for the bilinear form has been a research focus. Although there are numerous stopping criteria, they lack solid theoretical supports, and the reliability is unknown. In this paper, we consider the posteriori error estimates for the errors of approximate solutions of the matrix functions uTf(A)v. We derive an error expansion and prove that the first term of the error expansion can used as a reliable stopping criterion.

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