An accelerated conjugate gradient algorithm to compute low-lying eigenvalues -- a study for the Dirac operator in SU(2) lattice QCD

DOI10.1016/0010-4655(95)00126-3zbMath0917.65036arXivhep-lat/9507023OpenAlexW3124130186MaRDI QIDQ1276552

Thomas Kalkreuter, Hubert Simma

Publication date: 26 May 1999

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-lat/9507023

zbMATH Keywords

convergence accelerationeigenvectorsDirac operatorconjugate gradient methodWilson fermionsgauge fieldslow-lying eigenvaluessparse Hermitian matrix

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Yang-Mills and other gauge theories in quantum field theory (81T13) Strong interaction, including quantum chromodynamics (81V05) Quantum field theory on lattices (81T25) PDEs in connection with quantum mechanics (35Q40)

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Cites Work

• Computing eigenvalues of very large symmetric matrices. An implementation of a Lanczos algorithm with no reorthogonalization
• The Jacobi method for real symmetric matrices
• Almost diagonal matrices with multiple or close eigenvalues
• The computational efficiency of a new minimization algorithm for eigenvalue analysis
• Optimal gradient minimization scheme for finite element eigenproblems
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