On the spectrum of noisy blown-up matrices

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2020-01-01 DOI:10.1515/spma-2020-0010

I. Fazekas, Sándor Pecsora

引用次数: 1

Abstract

Abstract We study the eigenvalues of large perturbed matrices. We consider a pattern matrix P, we blow it up to get a large block-matrix Bn. We can observe only a noisy version of matrix Bn. So we add a random noise Wn to obtain the perturbed matrix An = Bn + Wn. Our aim is to find the structural eigenvalues of An. We prove asymptotic theorems on this problem and also suggest a graphical method to distinguish the structural and the non-structural eigenvalues of An.

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噪声放大矩阵的谱

摘要我们研究了大扰动矩阵的特征值。我们考虑一个模式矩阵P，我们把它分解得到一个大的块矩阵Bn。我们只能观察到矩阵Bn的一个有噪声的版本。所以我们加上一个随机噪声Wn，得到扰动矩阵An=Bn+Wn。我们的目的是找到An的结构特征值。我们证明了这个问题的渐近定理，并提出了一种区分An结构特征值和非结构特征值的图解方法。

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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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.