Improved lower bounds for the convergence radius ofRS-perturbation theory

1968 ◽  
Vol 2 (1) ◽  
pp. 101-107 ◽  
Author(s):  
W. A. Bingel
Keyword(s):  
Perturbation Theory ◽  
Lower Bounds ◽  
Convergence Radius

scholarly journals Eigenelements of perturbed operators

1990 ◽  
Vol 49 (1) ◽  
pp. 138-148 ◽  
Author(s):  
B. V. Limaye ◽  
M. T. Nair
Keyword(s):  
Lower Bound ◽  
Power Series ◽  
Lower Bounds ◽  
Spectral Projection ◽  
Linear Perturbation ◽  
Convergence Radius

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).

Complementary variational principles in perturbation theory

1968 ◽  
Vol 303 (1475) ◽  
pp. 503-509 ◽  
Keyword(s):  
Perturbation Theory ◽  
Lower Bound ◽  
Harmonic Oscillator ◽  
Lower Bounds ◽  
Upper Bound ◽  
Variational Principles ◽  
Upper And Lower Bounds ◽  
Quantum Mechanical ◽  
Simple Application ◽  
Mechanical Perturbation

Complementary upper and lower bounds are derived for second-order quantum-mechanical perturbation energies. The upper bound is equivalent to that of Hylleraas. The lower bound appears to be new, but reduces to that of Prager & Hirschfelder if a certain constraint is applied. A simple application to a perturbed harmonic oscillator is presented.

Force Reconstruction for Uncertain Structure Based on Interval Model and Second-Order Perturbation Theory

2019 ◽  
Vol 18 (01) ◽  
pp. 1950040
Author(s):  
Xiaowang Li ◽  
Haitao Zhao ◽  
Jiping Huang ◽  
Ji’an Chen
Keyword(s):  
Perturbation Theory ◽  
Lower Bounds ◽  
Second Order ◽  
Order Perturbation ◽  
Upper And Lower Bounds ◽  
Order Perturbation Theory ◽  
Uncertain Parameters ◽  
Interval Model ◽  
Uncertain Structure ◽  
Second Order Perturbation Theory

In order to reconstruct the upper and lower bounds of dynamic excitations applied on the uncertain structure, an algorithm based on interval model and second-order perturbation theory is presented in this paper. First, interval model is built up by expressing the uncertain parameters of structure in interval form. Next according to second-order perturbation theory, structure characteristic matrices and input force vector are approximated as second-order Taylor polynomial expansion at the midpoint of uncertain parameters. After that the input force’s midpoint, first-order and second-order partial derivatives are respectively calculated by existing step-by-step integration method. Then addition and subtraction of the three components obtained in previous step are operated. Ultimately the upper and lower bounds of dynamic load can be identified. Numerical simulation results demonstrate this method is with the characteristic of high efficiency and precision. In addition, it is able to remain a relatively strong robustness under noise turbulence.

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