用矩阵符号函数解(广义)周期Sylvester方程

doi:10.12286/jssx.2012.2.153

计算数学 ›› 2012, Vol. 34 ›› Issue (2): 153-162.DOI: 10.12286/jssx.2012.2.153

用矩阵符号函数解(广义)周期Sylvester方程

陈小山

华南师范大学数学科学学院, 广州 510631

收稿日期:2011-06-30 出版日期:2012-05-15 发布日期:2012-05-20
基金资助:
高等学校博士学科点专项科研基金项目(20104407110001),中山大学广东省计算科学重点实验室开放基金项目(201106005), 省科技攻关项目(2011B010200027)和省自然科学基金项目(S2011040003243).

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陈小山. 用矩阵符号函数解(广义)周期Sylvester方程[J]. 计算数学, 2012, 34(2): 153-162.

Chen Xiaoshan. SOLVING THE (GENERALIZED) PERIODIC SYLVESTER EQUATION WITH THE MATRIX SIGN FUNCTION[J]. Mathematica Numerica Sinica, 2012, 34(2): 153-162.

SOLVING THE (GENERALIZED) PERIODIC SYLVESTER EQUATION WITH THE MATRIX SIGN FUNCTION

Chen Xiaoshan

School of Mathematics, South China Normal University, Guangzhou 510631, China

Received:2011-06-30 Online:2012-05-15 Published:2012-05-20

(广义)周期Sylvester方程来源于周期离散线性系统. 本文主要研究这类方程满足特征值分别位于开左半复平面和开右半复平面或位于单位圆周内和单位圆周外条件时用矩阵符号函数求解的数值方法.并通过数值例子说明我们的结论.

关键词： 矩阵符号函数, (广义)周期Sylvester方程, Newton迭代

The (generalized) periodic Sylvester equation arises from linear periodic discrete-time systems. This paper is devoted to use the matrix sign function to solve (generalized) periodic Sylvester equations, which eigenvalues are contained in the open left half complex plane and the open right half complex plane or inside the unit circle and outside the unit circle. A numerical example illustrates our results.

Key words: The matrix sign function, (generalized) periodic Sylvester equations, Newton iteration

MR(2010)主题分类:

65F10

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摘要

用矩阵符号函数解(广义)周期Sylvester方程

SOLVING THE (GENERALIZED) PERIODIC SYLVESTER EQUATION WITH THE MATRIX SIGN FUNCTION

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