Density-Matrix-Based Algorithm for Solving Eigenvalue Problems
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TLDR
A new numerical algorithm for solving the symmetric eigenvalue problem is presented, which takes its inspiration from the contour integration and density matrix representation in quantum mechanics.Abstract:
A fast and stable numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques and takes its inspiration from the contour integration and density-matrix representation in quantum mechanics. It will be shown that this algorithm---named FEAST---exhibits high efficiency, robustness, accuracy, and scalability on parallel architectures. Examples from electronic structure calculations of carbon nanotubes are presented, and numerical performances and capabilities are discussed.read more
Citations
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An integral method for solving nonlinear eigenvalue problems
TL;DR: In this paper, a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane is proposed.
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The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science
Andreas Marek,Volker Blum,Volker Blum,R. Johanni,Ville Havu,Bruno Lang,T. Auckenthaler,Alexander Heinecke,Hans-Joachim Bungartz,Hermann Lederer +9 more
TL;DR: The Eigenvalue soLvers for Petascale Applications (ELPA) as discussed by the authors is a library for solving symmetric and Hermitian eigenvalue problems for dense matrices that have real-valued and complex-valued matrix entries.
Journal ArticleDOI
Parallel solution of partial symmetric eigenvalue problems from electronic structure calculations
T. Auckenthaler,Volker Blum,Hans-Joachim Bungartz,Thomas Huckle,R. Johanni,Lukas Krämer,Bruno Lang,Hermann Lederer,Paul R. Willems +8 more
TL;DR: In this article, the tridiagonal-to-banded back transformation was proposed to improve the parallel efficiency for large numbers of processors as well as the per-processor utilization.
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Efficient estimation of eigenvalue counts in an interval
TL;DR: In this paper, the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is estimated using polynomial and rational approximation filtering combined with a stochastic procedure.
References
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Journal ArticleDOI
Density-functional method for nonequilibrium electron transport
TL;DR: In this paper, an ab initio method for calculating the electronic structure, electronic transport, and forces acting on the atoms, for atomic scale systems connected to semi-infinite electrodes and with an applied voltage bias.
Book
Lapack Users' Guide
TL;DR: The third edition of LAPACK provided a guide to troubleshooting and installation of Routines, as well as providing examples of how to convert from LINPACK or EISPACK to BLAS.
MonographDOI
ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods
TL;DR: The Arnoldi factorization, the implicitly restarted Arnoldi method: structure of the Eigenvalue problem Krylov subspaces and projection methods, and more.
Journal ArticleDOI
Ab initio modeling of quantum transport properties of molecular electronic devices
Jeremy Taylor,Hong Guo,Jian Wang +2 more
TL;DR: In this paper, a self-consistent ab initio technique for modeling quantum transport properties of atomic and molecular scale nanoelectronic devices under external bias potentials was proposed, based on density functional theory using norm conserving nonlocal pseudopotentials to define the atomic core and nonequilibrium Green's functions (NEGF's) to calculate the charge distribution.
Book
Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide
TL;DR: This book discusses iterative projection methods for solving Eigenproblems, and some of the techniques used to solve these problems came from the literature on Hermitian Eigenvalue.