Eigenvalue Problems for a Class of Infinite Complex Symmetric Tridiagonal Matrices with Related Three-Term Recurrence Relation
Eigenvalue Problems for a Class of Infinite Complex Symmetric Tridiagonal Matrices with Related Three-Term Recurrence Relation
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一类具有相关三项递推关系的无限复对称三对角矩阵的特征值问题
DOI：
10.1016/j.cam.2021.113964
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发表时间：
2022
影响因子：
2.4
通讯作者：
Y. Miyazaki
中科院分区：
文献类型：
--
作者：
N. Asai;Y. Miyazaki
本文研究了一类无限复对称三对角矩阵的特征值问题，其对角元和非对角元的模是发散的，且有一个紧逆。我们把矩阵看作是一个线性算子，它把Hilbert空间中的极大域从λ 2映射到λ 2。本文推广了Ikebe等人关于一类特征值问题的工作，并得到了其渐近误差估计。本文主要研究以下几个问题：（1）考虑哪一类三项递推关系的找零问题可以转化为上述无限三对角矩阵类的特征值问题;（2）确定一类矩阵，利用截主子矩阵的特征值可以保证得到好的近似特征值;（3）确定一类矩阵，使我们能得到（2）中计算的渐近误差估计。
We consider the eigenvalue problem of a class of infinite complex symmetric tridiagonal matrices whose diagonal and off-diagonal elements diverge in modulus, and which have a compact inverse. We regard the matrix as a linear operator mapping a maximal domain in Hilbert space ℓ 2 into ℓ 2. This paper aims to extend the work of Ikebe et al. on a class of eigenvalue problems and for which asymptotic error estimates have been obtained. In this paper we focus on the following points:(1) considering what class of zero-finding problems of three-term recurrence relations can be reformulated as eigenvalue problems of the class of infinite tridiagonal matrices stated above;(2) determining a class of matrices for which obtaining good approximate eigenvalues is guaranteed by using those of truncated principal sub-matrices; and (3) determining a class of matrices that permits us the asymptotic error estimates computed as in (2).