The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of J0(z) - iJ1(z) and of Bessel functions Jm(z) of any real order m
The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of J0(z) - iJ1(z) and of Bessel functions Jm(z) of any real order m
复制标题
无限紧复对称矩阵的特征值问题及其应用于 J0(z) - iJ1(z) 复零点和任意实数 m 阶贝塞尔函数 Jm(z) 的数值计算
DOI：
10.1016/0024-3795(93)90112-2
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发表时间：
1993
影响因子：
1.1
通讯作者：
Minoru Harada
中科院分区：
文献类型：
--
作者：
Y. Ikebe;Yasushi Kikuchi;I. Fujishiro;Nobuyoshi Asai;K. Takanashi;Minoru Harada
考虑通过计算截断的有限矩阵的特征值并取一个明显的极限来计算一个给定的紧无穷矩阵的简单特征值（看作是在复希尔伯特空间中运算）。在本文中，我们处理一个特殊的情况，即给定的矩阵是紧、复和对称的（但不一定是厄米矩阵）。研究了两个应用实例。第一个是关于在分析斜坡滩上的孤立波时出现的方程j0 (z)−iJ1(z)=0，第二个是关于任意实阶贝塞尔函数jm (z)的零点。在每种情况下，问题被重新表述为一个紧复对称三对角矩阵算子in2的特征值问题，其特征值都是简单的。在本文所证明的一般定理的基础上，给出了截断数值解的完整误差分析，证明了很少使用的广义瑞利商的实用性。
Consider computing simple eigenvalues of a given compact infinite matrix re- garded as operating in the complex Hilbert spacel2by computing the eigenvalues of the truncated finite matrices and taking an obvious limit. In this paper we deal with a special case where the given matrix is compact, complex, and symmetric (but not necessarily Hermitian). Two examples of application are studied. The first is con- cerned with the equationJ0(z) −iJ1(z)=0 appearing in the analysis of the solitary-wave runup on a sloping beach, and the second with the zeros of the Bessel functionJm(z) of any real orderm. In each case, the problem is reformulated as an eigenvalue problem for a compact complex symmetric tridiagonal matrix operator inl2whose eigenvalues are all simple. A complete error analysis for the numerical solution by truncation is given, based on the general theorems proved in this paper, where the usefulness of the seldom used generalized Rayleigh quotient is demonstrated.