周期二维广义系统

IF 0.7 4区 数学 Q2 Mathematics
P. Benner, P. Van Dooren
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引用次数: 0

摘要

在本文中,我们分析了具有周期系数的二维广义系统的相容性条件,并导出了一个特殊的坐标系,在该坐标系中,这些条件归结为简单的矩阵交换性条件。我们还证明,在这样一个周期性的2D描述符系统中,不同轨迹的兼容性可以很好地用所谓的规则铅笔的矩阵关系来表示,这些关系在[Benner和Byers.An algorithm for matrix pences:Theory and new algorithms.Number.Math.,103(4):539-5732006]中介绍。然后,我们证明了这些思想可以推广到多维周期广义系统,并简要讨论了复系数矩阵和实系数矩阵情况之间的区别。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Periodic two-dimensional descriptor systems
In this note, we analyze the compatibility conditions of 2D descriptor systems with periodic coefficients and we derive a special coordinate system in which these conditions reduce to simple matrix commutativity conditions. We also show that the compatibility of the different trajectories in such a periodic 2D descriptor system can elegantly be formulated in terms of so-called matrix relations of regular pencils, which were introduced in [Benner and Byers. An arithmetic for matrix pencils: Theory and new algorithms. Numer. Math., 103(4):539-573, 2006]. We then show that these ideas can be extended to multidimensional periodic descriptor systems and briefly discuss the difference between the case of complex and real coefficient matrices.
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来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
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