JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices

Bollhöfer, Matthias; Notay, Yvan

doi:10.1016/j.cpc.2007.08.004

Cited by 110 publications

(84 citation statements)

References 52 publications

(89 reference statements)

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“…Here we extend those calculations to quasibound states up to L = 40 and to the first three excited vibrational states. The main reason making this extension possible is a better technique for searching the eigenvalues of a large sparse matrix [32] and faster personal computers.…”

Section: Lagrange-mesh Methodsmentioning

confidence: 99%

Quadrupole Transitions in the Bound Rotational-Vibrational Spectrum of the Hydrogen Molecular Ion

Pilón

Baye

2012

Few-Body Syst

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Abstract. The three-body Schrödinger equation of the H + 2 hydrogen molecular ion with Coulomb potentials is solved in perimetric coordinates using the Lagrange-mesh method. The Lagrange-mesh method is an approximate variational calculation with variational accuracy and the simplicity of a calculation on a mesh. Energies and wave functions of up to four of the lowest vibrational bound or quasibound states for total orbital momenta from 0 to 40 are calculated. The obtained energies have an accuracy varying from about 13 digits for the lowest vibrational state to at least 9 digits for the third vibrational excited state. With the corresponding wave functions, a simple calculation using the associated Gauss quadrature provides accurate quadrupole transition probabilities per time unit between those states over the whole rotational bands. Extensive results are presented with six significant figures.

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Section: Lagrange-mesh Methodsmentioning

confidence: 99%

Quadrupole Transitions in the Bound Rotational-Vibrational Spectrum of the Hydrogen Molecular Ion

Pilón

Baye

2012

Few-Body Syst

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“…Due the orthogonality constraint X T X = I, the linear independence constraint qualification always holds true for (2). Therefore, the first-order necessary conditions for optimality of (2) are that…”

Section: Preliminariesmentioning

confidence: 99%

“…Specifically, in addition to the usual subspace iteration in which the current iterate of X is multiplied by AA T , we also solve a restricted version of (2) in a subspace spanned by a few previous iterates of X. For example, at iteration i, we may add an extra subspace constraint to (2) so that…”

Section: During Decades Of Research Numerous Iterative Algorithms Hamentioning

confidence: 99%

“…The classic simple subspace, or simultaneous, iteration method, extends the idea of the power method which computes the largest eigenvalue and its eigenvector (see [16,17,24,26] for example), performing repeated matrix multiplication followed by orthogonalization. More elaborative algorithms including Arnoldi methods [14,13], Lanczos methods [21,12], Jacobi-Davidson methods [23,2], to cite a few for each type, are specifically designed for large-scale but sparse matrices or other types of structured matrices.…”

Section: During Decades Of Research Numerous Iterative Algorithms Hamentioning

confidence: 99%

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Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions

Liu¹,

Wen²,

Zhang³

2012

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In many data-intensive applications, the use of principal component analysis (PCA) and other related techniques is ubiquitous for dimension reduction, data mining or other transformational purposes. Such transformations often require efficiently, reliably and accurately computing dominant singular value decompositions (SVDs) of large unstructured matrices. In this paper, we propose and study a subspace optimization technique to significantly accelerate the classic simultaneous iteration method. We analyze the convergence of the proposed algorithm, and numerically compare it with several state-of-the-art SVD solvers under the MATLAB environment. Extensive computational results show that on a wide range of large unstructured matrices, the proposed algorithm can often provide improved efficiency or robustness over existing algorithms.

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“…Therefore, it is possible to use Lanzcos or Davidson type diagonalization routines that (iteratively) provide a small number of eigenstates within a specific energy interval. Here we adopted the Davidson-based diagonalization routine JADAMILU [63] that is especially designed for the efficient diagonalization of large sparse matrices.…”

Section: Exact Diagonalization (Configuration Interaction)mentioning

confidence: 99%

Theoretical description of two ultracold atoms in finite three-dimensional optical lattices using realistic interatomic interaction potentials

2011

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A theoretical approach is described for an exact numerical treatment of a pair of ultracold atoms interacting via a central potential that are trapped in a finite three-dimensional optical lattice. The coupling of center-of-mass and relative-motion coordinates is treated using an exact diagonalization (configuration-interaction) approach. The orthorhombic symmetry of an optical lattice with three different but orthogonal lattice vectors is explicitly considered as is the Fermionic or Bosonic symmetry in the case of indistinguishable particles.

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JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices

Cited by 110 publications

References 52 publications

Quadrupole Transitions in the Bound Rotational-Vibrational Spectrum of the Hydrogen Molecular Ion

Quadrupole Transitions in the Bound Rotational-Vibrational Spectrum of the Hydrogen Molecular Ion

Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions

Theoretical description of two ultracold atoms in finite three-dimensional optical lattices using realistic interatomic interaction potentials

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