Computation of Large-Dimension Jordan Normal Transform via Popular Platforms

被引：0
作者：
Chunxiao Shi
Yong-Cong Chen
Xia Xiong
Ping Ao
机构：
[1] Shanghai University,Shanghai Center for Quantitative Life Sciences and Physics Department
来源：
Journal of Nonlinear Mathematical Physics | 2023年 / 30卷
关键词：
Large-dimension Jordan normal transform; Jordan matrix; Lyapunov function; Eigenvalue; (Generalized) Eigenvector;
D O I：
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中图分类号：
学科分类号：
摘要：
We address the practical issue that popular computation platforms like Matlab©\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\copyright }$$\end{document} are unable to perform the Jordan normal (canonical) form J and the associated transform matrix P on a high-dimension matrix. Given the knowledge of the eigenvalues and eigenvectors of n-square matrix A obtained on these platforms, we present an efficient algorithm of Jordan transform with detailed computation steps. The efficiency is demonstrated by comparing the simulation results of 11 examples with varying orders of n to that computed by the symbolic-based and capacity-limited routine [P,J]=jordan(A)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[P, J] = {\textsf {jordan}}(A)$$\end{document} in Matlab©\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\copyright }$$\end{document}. Applications in stochastic dynamics are addressed.
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页码：834 / 842
页数：8
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