Search results for "Lanczos resampling"

showing 3 items of 3 documents

Fluctuations in mesoscopic systems

1992

Abstract Electronic wavefunctions in weakly disordered systems have been studied within the Anderson model of localization. The eigenstates calculated by means of the Lanczos diagonalization algorithm display characteristic spatial fluctuations that can be described by a multifractal analysis. For increasing disorder or energy the observed curdling of the wavefunction reflects the stronger localization, but no exponential decay can be observed. This is reflected in the set of generalized fractal dimensions and the singularity spectrum of the fractal measure.

PhysicsLanczos resamplingMesoscopic physicsFractalGeneral Chemical EngineeringQuantum mechanicsGeneral Physics and AstronomyMultifractal systemExponential decaySingularity spectrumCondensed Matter::Disordered Systems and Neural NetworksAnderson impurity modelFractal dimensionPhilosophical Magazine B
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Solution of time-independent Schrödinger equation by the imaginary time propagation method

2007

Numerical solution of eigenvalues and eigenvectors of large matrices originating from discretization of linear and non-linear Schrodinger equations using the imaginary time propagation (ITP) method is described. Convergence properties and accuracy of 2nd and 4th order operator-splitting methods for the ITP method are studied using numerical examples. The natural convergence of the method is further accelerated with a new dynamic time step adjustment method. The results show that the ITP method has better scaling with respect to matrix size as compared to the implicitly restarted Lanczos method. An efficient parallel implementation of the ITP method for shared memory computers is also demons…

Numerical AnalysisPhysics and Astronomy (miscellaneous)DiscretizationApplied MathematicsMathematical analysisMathematicsofComputing_NUMERICALANALYSISOrder (ring theory)Computer Science::Human-Computer InteractionComputer Science ApplicationsSchrödinger equationComputational Mathematicssymbols.namesakeLanczos resamplingShared memoryModeling and SimulationConvergence (routing)symbolsScalingEigenvalues and eigenvectorsMathematicsJournal of Computational Physics
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Computation of a few smallest eigenvalues of elliptic operators using fast elliptic solvers

2001

The computation of a few smallest eigenvalues of generalized algebraic eigenvalue problems is studied. The considered problems are obtained by discretizing self-adjoint second-order elliptic partial differential eigenvalue problems in two- or three-dimensional domains. The standard Lanczos algorithm with the complete orthogonalization is used to compute some eigenvalues of the inverted eigenvalue problem. Under suitable assumptions, the number of Lanczos iterations is shown to be independent of the problem size. The arising linear problems are solved using some standard fast elliptic solver. Numerical experiments demonstrate that the inverted problem is much easier to solve with the Lanczos…

Applied MathematicsNumerical analysisMathematical analysisMathematicsofComputing_NUMERICALANALYSISGeneral EngineeringLanczos algorithmElliptic curveLanczos resamplingElliptic operatorMultigrid methodComputational Theory and MathematicsModeling and SimulationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONOrthogonalizationSoftwareEigenvalues and eigenvectorsMathematicsCommunications in Numerical Methods in Engineering
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