Block tridiagonal matrix inversion and fast transmission calculations
نویسندگان
چکیده
A method for the inversion of block tridiagonal matrices encountered in electronic structure calculations is developed, with the goal of efficiently determining the matrices involved in the Fisher–Lee relation for the calculation of electron transmission coefficients. The new method leads to faster transmission calculations compared to traditional methods, as well as freedom in choosing alternate Green’s function matrix blocks for transmission calculations. The new method also lends itself to calculation of the tridiagonal part of the Green’s function matrix. The effect of inaccuracies in the electrode self-energies on the transmission coefficient is analyzed and reveals that the new algorithm is potentially more stable towards such inaccuracies. 2007 Elsevier Inc. All rights reserved. PACS: 71.15. m; 02.70. c
منابع مشابه
Block Tridiagonal Matrices in Electronic Structure Calculations
A method for the inversion of block tridiagonal matrices encountered in electronic structure calculations is developed, with the goal of efficiently determining the matrices involved in the Fisher–Lee relation for the calculation of electron transmission coefficients. The new method leads to faster transmission calculations compared to traditional methods, as well as freedom in choosing alterna...
متن کاملEigendecomposition of Block Tridiagonal Matrices
Block tridiagonal matrices arise in applied mathematics, physics, and signal processing. Many applications require knowledge of eigenvalues and eigenvectors of block tridiagonal matrices, which can be prohibitively expensive for large matrix sizes. In this paper, we address the problem of the eigendecomposition of block tridiagonal matrices by studying a connection between their eigenvalues and...
متن کاملCharacterizing the inverses of block tridiagonal, block Toeplitz matrices
We consider the inversion of block tridiagonal, block Toeplitz matrices and comment on the behaviour of these inverses as one moves away from the diagonal. Using matrix Möbius transformations, we first present an O(1) representation (with respect to the number of block rows and block columns) for the inverse matrix and subsequently use this representation to characterize the inverse matrix. The...
متن کاملThe Scheduling of a Parallel Tiled Matrix Inversion Algorithm
The non equilibrium Green’s function method used in density functional theory based methods for computing electron transport at nano scale requires repeated inversions of a large block tridiagonal matrix. This calculation constitutes a substantial part of the total execution time, and therefore an efficient special method for the block tridiagonal matrix inversion was developed recently. This p...
متن کاملInversion of general tridiagonal matrices
In the current work, the authors present a symbolic algorithm for finding the inverse of any general nonsingular tridiagonal matrix. The algorithm is mainly based on the work presented in [Y. Huang, W.F. McColl, Analytic inversion of general tridiagonal matrices, J. Phys. A 30 (1997) 7919–7933] and [M.E.A. El-Mikkawy, A fast algorithm for evaluating nth order tridiagonal determinants, J. Comput...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comput. Physics
دوره 227 شماره
صفحات -
تاریخ انتشار 2008