Variational Bounds to Eigenvalues of Self-Adjoint Eigenvalue Problems with Arbitrary Spectrum
Variational Bounds to Eigenvalues of Self-Adjoint Eigenvalue Problems with Arbitrary Spectrum
复制标题
任意谱自伴特征值问题特征值的变分界
DOI：
10.4171/zaa/677
复制
发表时间：
1995
影响因子：
1.2
通讯作者：
U. Mertins
中科院分区：
文献类型：
--
作者：
S. Zimmermann;U. Mertins
。本文将Lehmann-Maehly和Goerisch的方法推广到具有任意本质谱的自伴本征值问题。这种扩展是通过随后利用该方法的局部特性来获得的。通过这种方法，得到了所有孤立本征值的上下界。在我们的证明中，与Wielandt逆迭代的密切关系变得非常明显。
. In the present paper a method by Lehmann-Maehly and Goerisch is extended to self-adjoint eigenvalue problems with arbitrary essential spectrum. This extension is obtained by consequently making use of the local character of the method. In this way, upper and lower bounds to all isolated eigenvalues are derived. In our proofs, the close relationship to Wielandt’s inverse iteration becomes quite obvious.