Design and Implementation of Parallel Counterpropagation Networks Using MPI

Margaris, Athanasios; Souravlas, Stavros; Kotsialos, Efthimios; Roumeliotis, Μanos

doi:10.15388/informatica.2007.165

Cited by 4 publications

(1 citation statement)

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“…It seems likely that this algorithm could be parallelized in essentially the same manner as the Jacobi eigenvalue algorithm 44 . Additionally, we suspect that higher-order extensions are possible, such as treating η as piecewise linear instead of piecewise constant.…”

Section: Methodsmentioning

confidence: 99%

Stable unitary integrators for the numerical implementation of continuous unitary transformations

Savitz

Refael

2017

Phys. Rev. B

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The technique of continuous unitary transformations has recently been used to provide physical insight into a diverse array of quantum mechanical systems. However, the question of how to best numerically implement the flow equations has received little attention. The most immediately apparent approach, using standard Runge-Kutta numerical integration algorithms, suffers from both severe inefficiency due to stiffness and the loss of unitarity. After reviewing the formalism of continuous unitary transformations and Wegner's original choice for the infinitesimal generator of the flow, we present a number of approaches to resolving these issues including a choice of generator which induces what we call the "uniform tangent decay flow" and three numerical integrators specifically designed to perform continuous unitary transformations efficiently while preserving the unitarity of flow. We conclude by applying one of the flow algorithms to a simple calculation that visually demonstrates the many-body localization transition.

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Section: Methodsmentioning

confidence: 99%