scholarly journals Legendre multi-projection methods for solving eigenvalue problems for a compact integral operator

2013 ◽  
Vol 239 ◽  
pp. 135-151 ◽  
Author(s):  
Bijaya Laxmi Panigrahi ◽  
Guangqing Long ◽  
Gnaneshwar Nelakanti
Keyword(s):  
Integral Operator ◽  
Eigenvalue Problems ◽  
Projection Methods ◽  
Compact Integral Operator

Analysis And Efficient Solution Of Stationary Schrödinger Equation Governing Electronic States Of Quantum Dots And Rings In Magnetic Field

2012 ◽  
Vol 11 (5) ◽  
pp. 1591-1617 ◽  
Author(s):  
Marta M. Betcke ◽  
Heinrich Voss
Keyword(s):  
Magnetic Field ◽  
Eigenvalue Problems ◽  
Rotational Symmetry ◽  
Electronic States ◽  
Nonlinear Problems ◽  
Projection Methods ◽  
Computational Time ◽  
Arnoldi Method ◽  
Nonlinear Eigenvalue Problems ◽  
The One

AbstractIn this work the one-band effective Hamiltonian governing the electronic states of a quantum dot/ring in a homogenous magnetic field is used to derive a pair/quadruple of nonlinear eigenvalue problems corresponding to different spin orientations and in case of rotational symmetry additionally to quantum number -L•i. We show, that each of those pair/quadruple of nonlinear problems allows for the min-max characterization of its eigenvalues under certain conditions, which are satisfied for our examples and the common InAs/GaAs heterojunction. Exploiting the minmax property we devise efficient iterative projection methods simultaneously handling the pair/quadruple of nonlinear problems and thereby saving up to 40% of the computational time as compared to the nonlinear Arnoldi method applied to each of the problems separately.

scholarly journals A New Algorithm for Solving Large-Scale Generalized Eigenvalue Problem Based on Projection Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
F. Abbasi Nedamani ◽  
A. H. Refahi Sheikhani ◽  
H. Saberi Najafi
Keyword(s):  
Numerical Stability ◽  
Large Scale ◽  
Eigenvalue Problems ◽  
Projection Methods ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Problems ◽  
Ritz Procedure ◽  
The Moment ◽  
Block Version ◽  
Methods Numerical

In this paper, we consider four methods for determining certain eigenvalues and corresponding eigenvectors of large-scale generalized eigenvalue problems which are located in a certain region. In these methods, a small pencil that contains only the desired eigenvalue is derived using moments that have obtained via numerical integration. Our purpose is to improve the numerical stability of the moment-based method and compare its stability with three other methods. Numerical examples show that the block version of the moment-based (SS) method with the Rayleigh–Ritz procedure has higher numerical stability than respect to other methods.

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