Computing entries of the inverse of a sparse matrix using the FIND algorithm

DOI10.1016/j.jcp.2008.06.033zbMath1214.82124OpenAlexW2116452365WikidataQ57369279 ScholiaQ57369279MaRDI QIDQ955257

B. E. Eshmatov

Publication date: 19 November 2008

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2008.06.033

zbMATH Keywords

Green's functionGaussian eliminationsparse matrixnested dissectionnanotransistorNEGFsemiconductor field-effect transistor

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Statistical mechanics of semiconductors (82D37) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (14)

A hybrid method for the parallel computation of Green's functions ⋮ Fast Sparse Selected Inversion ⋮ Improvements on non-equilibrium and transport Green function techniques: the next-generation Transiesta ⋮ A fast algorithm for sparse matrix computations related to inversion ⋮ A nested dissection approach to modeling transport in nanodevices: Algorithms and applications ⋮ Parallelized integrated nested Laplace approximations for fast Bayesian inference ⋮ Extension and optimization of the FIND algorithm: Computing Green's and less-than Green's functions ⋮ A two-dimensional domain decomposition technique for the simulation of quantum-scale devices ⋮ Finding off‐diagonal entries of the inverse of a large symmetric sparse matrix ⋮ A probing method for computing the diagonal of a matrix inverse ⋮ An approximate framework for quantum transport calculation with model order reduction ⋮ Efficient Covariance Approximations for Large Sparse Precision Matrices ⋮ Numerical methods for Kohn–Sham density functional theory ⋮ An Uncertainty-Weighted Asynchronous ADMM Method for Parallel PDE Parameter Estimation

Cites Work

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• Reduktionsverfahren für Differenzengleichungen bei Randwertaufgaben. I
• Inverse Iteration, Ill-Conditioned Equations and Newton’s Method
• On computing certain elements of the inverse of a sparse matrix
• A DIRECT SOLUTION TO THE BLOCK TRIDIAGONAL MATRIX INVERSION PROBLEM
• The Calculation of the Eigenvectors of a General Complex Matrix by Inverse Iteration
• On Direct Methods for Solving Poisson’s Equations
• Nested Dissection of a Regular Finite Element Mesh

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