具有给定特征值的结构化矩阵的数值构造

IF 1 Q2 MATHEMATICS

Special Matrices Pub Date : 2019-01-01 DOI:10.1515/spma-2019-0020

Brian D. Sutton

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引用次数: 0

摘要

摘要考虑一个结构特征值反问题，其中实对称矩阵的特征值是指定的，所选的项可以被约束为特定的数值或非零。这包括指定矩阵图的问题，这是由零和非零项的位置决定的。本文给出了构造结构特征值反问题解的一种数值方法。将该问题转化为正交流形上的约束优化问题，并用数值优化程序寻求其解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Numerical construction of structured matrices with given eigenvalues

Abstract We consider a structured inverse eigenvalue problem in which the eigenvalues of a real symmetric matrix are specified and selected entries may be constrained to take specific numerical values or to be nonzero. This includes the problem of specifying the graph of the matrix, which is determined by the locations of zero and nonzero entries. In this article, we develop a numerical method for constructing a solution to the structured inverse eigenvalue problem. The problem is recast as a constrained optimization problem over the orthogonal manifold, and a numerical optimization routine seeks its solution.

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来源期刊

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.