Determination of eigenstates via Lanczos-based forward substitution and filter- diagonalization

DOI10.1006/jcph.1997.5777zbMath0905.65049OpenAlexW1965934268MaRDI QIDQ1372009

Hua Guo, Rongqing Chen

Publication date: 9 February 1999

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcph.1997.5777

zbMATH Keywords

filteringLanczos algorithminverse iterationLanczos iterationquantum eigenstateseigenstates in energy range

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Estimates of eigenvalues in context of PDEs (35P15) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Bethe-Salpeter and other integral equations arising in quantum theory (81Q40)

Related Items (1)

The Chebyshev propagator for quantum systems

Cites Work

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• A Fourier method solution for the time dependent Schrödinger equation as a tool in molecular dynamics
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Computing eigenvalues of very large symmetric matrices. An implementation of a Lanczos algorithm with no reorthogonalization
• Nonadiabatic processes in condensed matter: Semi-classical theory and implementation
• Kernel polynomial approximations for densities of states and spectral functions
• An efficient Chebyshev-Lanczos method for obtaining eigensolutions of the Schrödinger equation on a grid
• Some History of the Conjugate Gradient and Lanczos Algorithms: 1948–1976
• The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems
• Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix
• Computational Variants of the Lanczos Method for the Eigenproblem

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