Abstract
AbstractLet λ0 be a semisimple eigenvalue of an operator T0. Let Γ0 be a circle with centre λs0 containing no other spectral value of T0. Some lower bounds are obtained for the convergence radius of the power series for the spectral projection P(t) and for trace T(t)P(t) associated with linear perturbation family T(t) = T0 + tV0 and the circle Γ0. They are useful when T0 is a member of a sequence (Tn) which approximates an operator T in a collectively compact manner. These bounds result from a modification of Kato's method of majorizing series, based on an idea of Redont. I λ0 is simple, it is shown that the same lower bound are valid for the convergence radius of a power series yielding an eigenvector of T(t).
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics,Statistics and Probability
Reference7 articles.
1. On the accuracy of the Rayleigh-Schrödinger approximations
2. On the error estimates for the Rayleigh-Schrödinger series and the Kato-Rellich perturbation series
3. [7] Redont P. , Application de la théorie de la perturbation des opérateurs linéaires à l'obtention de bornes d'erreur sur les éléments propres et à leur calcul, (Thése Doct.-Ing., Univ. de Grenoble, 1979).
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. The projection Kantorovich method for eigenvalue problems;Journal of Computational and Applied Mathematics;1994-05