Relevant bibliographies by topics / Block tridiagonal matrix

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Academic literature on the topic 'Block tridiagonal matrix'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Block tridiagonal matrix"

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Zgirouski, A. A., and N. A. Likhoded. "Modified method of parallel matrix sweep." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 4 (January 7, 2020): 425–34. http://dx.doi.org/10.29235/1561-2430-2019-55-4-425-434.

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The topic of this paper refers to efficient parallel solvers of block-tridiagonal linear systems of equations. Such systems occur in numerous modeling problems and require usage of high-performance multicore computation systems. One of the widely used methods for solving block-tridiagonal linear systems in parallel is the original block-tridiagonal sweep method. We consider the algorithm based on the partitioning idea. Firstly, the initial matrix is split into parts and transformations are applied to each part independently to obtain equations of a reduced block-tridiagonal system. Secondly, the reduced system is solved sequentially using the classic Thomas algorithm. Finally, all the parts are solved in parallel using the solutions of a reduced system. We propose a modification of this method. It was justified that if known stability conditions for the matrix sweep method are satisfied, then the proposed modification is stable as well.
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Kim, Sang Wook, and Jae Heon Yun. "Block ILU factorization preconditioners for a block-tridiagonal H-matrix." Linear Algebra and its Applications 317, no. 1-3 (September 2000): 103–25. http://dx.doi.org/10.1016/s0024-3795(00)00146-4.

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Dub, P., and O. Litzman. "The Darwin procedure in optics of layered media and the matrix theory." Acta Crystallographica Section A Foundations of Crystallography 55, no. 4 (July 1, 1999): 613–20. http://dx.doi.org/10.1107/s010876739801513x.

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The Darwin dynamical theory of diffraction for two beams yields a nonhomogeneous system of linear algebraic equations with a tridiagonal matrix. It is shown that different formulae of the two-beam Darwin theory can be obtained by a uniform view of the basic properties of tridiagonal matrices, their determinants (continuants) and their close relationship to continued fractions and difference equations. Some remarks concerning the relation of the Darwin theory in the three-beam case to tridiagonal block matrices are also presented.
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Twig, Y., and R. Kastner. "Block tridiagonal matrix formulation for inhomogeneous penetrable cylinders." IEE Proceedings - Microwaves, Antennas and Propagation 144, no. 3 (1997): 184. http://dx.doi.org/10.1049/ip-map:19971152.

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Hirshman, S. P., K. S. Perumalla, V. E. Lynch, and R. Sanchez. "BCYCLIC: A parallel block tridiagonal matrix cyclic solver." Journal of Computational Physics 229, no. 18 (September 2010): 6392–404. http://dx.doi.org/10.1016/j.jcp.2010.04.049.

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Gündoğar, Zeynep, and Metin Demiralp. "Block tridiagonal matrix enhanced multivariance products representation (BTMEMPR)." Journal of Mathematical Chemistry 56, no. 3 (November 17, 2017): 747–69. http://dx.doi.org/10.1007/s10910-017-0828-7.

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Petersen, Dan Erik, Hans Henrik B. Sørensen, Per Christian Hansen, Stig Skelboe, and Kurt Stokbro. "Block tridiagonal matrix inversion and fast transmission calculations." Journal of Computational Physics 227, no. 6 (March 2008): 3174–90. http://dx.doi.org/10.1016/j.jcp.2007.11.035.

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Brimkulov, Ulan. "Matrices whose inverses are tridiagonal, band or block-tridiagonal and their relationship with the covariance matrices of a random Markov process." Filomat 33, no. 5 (2019): 1335–52. http://dx.doi.org/10.2298/fil1905335b.

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The article discusses the matrices of the form A1n, Amn, AmN, whose inverses are: tridiagonal matrix A-1n (n - dimension of the A-mn matrix), banded matrix A-mn (m is the half-width band of the matrix) or block-tridiagonal matrix A-m N (N = n x m - full dimension of the block matrix; m - the dimension of the blocks) and their relationships with the covariance matrices of measurements with ordinary (simple) Markov Random Processes (MRP), multiconnected MRP and vector MRP, respectively. Such covariance matrices frequently occur in the problems of optimal filtering, extrapolation and interpolation of MRP and Markov Random Fields (MRF). It is shown, that the structures of the matrices A1n, Amn, AmN have the same form, but the matrix elements in the first case are scalar quantities; in the second case matrix elements represent a product of vectors of dimension m; and in the third case, the off-diagonal elements are the product of matrices and vectors of dimension m. The properties of such matrices were investigated and a simple formulas of their inverses were found. Also computational efficiency in the storage and the inverse of such matrices have been considered. To illustrate the acquired results, an example on the covariance matrix inversions of two-dimensional MRP is given.
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Yun, Jae Heon. "Block incomplete factorization preconditioners for a symmetric block-tridiagonal M-matrix." Journal of Computational and Applied Mathematics 94, no. 2 (August 1998): 133–52. http://dx.doi.org/10.1016/s0377-0427(98)00078-8.

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Dette, Holger, Bettina Reuther, W. J. Studden, and M. Zygmunt. "Matrix Measures and Random Walks with a Block Tridiagonal Transition Matrix." SIAM Journal on Matrix Analysis and Applications 29, no. 1 (January 2007): 117–42. http://dx.doi.org/10.1137/050638230.

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Dissertations / Theses on the topic "Block tridiagonal matrix"

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Edvardsson, Elisabet. "Band structures of topological crystalline insulators." Thesis, Karlstads universitet, Institutionen för ingenjörsvetenskap och fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-65536.

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Topological insulators and topological crystalline insulators are materials that have a bulk band structure that is gapped, but that also have toplogically protected non-gapped surface states. This implies that the bulk is insulating, but that the material can conduct electricity on some of its surfaces. The robustness of these surface states is a consequence of time-reversal symmetry, possibly in combination with invariance under other symmetries, like that of the crystal itself. In this thesis we review some of the basic theory for such materials. In particular we discuss how topological invariants can be derived for some specific systems. We then move on to do band structure calculations using the tight-binding method, with the aim to see the topologically protected surface states in a topological crystalline insulator. These calculations require the diagonalization of block tridiagonal matrices. We finish the thesis by studying the properties of such matrices in more detail and derive some results regarding the distribution and convergence of their eigenvalues.
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Archid, Atika. "Méthodes par blocs adaptées aux matrices structurées et au calcul du pseudo-inverse." Thesis, Littoral, 2013. http://www.theses.fr/2013DUNK0394/document.

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Nous nous intéressons dans cette thèse, à l'étude de certaines méthodes numériques de type krylov dans le cas symplectique, en utilisant la technique de blocs. Ces méthodes, contrairement aux méthodes classiques, permettent à la matrice réduite de conserver la structure Hamiltonienne ou anti-Hamiltonienne ou encore symplectique d'une matrice donnée. Parmi ces méthodes, nous nous sommes intéressés à la méthodes d'Arnoldi symplectique par bloc que nous appelons aussi bloc J-Arnoldi. Notre but essentiel est d’étudier cette méthode de façon théorique et numérique, sur la nouvelle structure du K-module libre ℝ²nx²s avec K = ℝ²sx²s où s ≪ n désigne la taille des blocs utilisés. Un deuxième objectif est de chercher une approximation de l'epérateur exp(A)V, nous étudions en particulier le cas où A est une matrice réelle Hamiltonnienne et anti-symétrique de taille 2n x 2n et V est une matrice rectangulaire ortho-symplectique de taille 2n x 2s sur le sous-espace de Krylov par blocs Km(A,V) = blockspan {V,AV,...,Am-1V}, en conservant la structure de la matrice V. Cette approximation permet de résoudre plusieurs problèmes issus des équations différentielles dépendants d'un paramètre (EDP) et des systèmes d'équations différentielles ordinaires (EDO). Nous présentons également une méthode de Lanczos symplectique par bloc, que nous nommons bloc J-Lanczos. Cette méthode permet de réduire une matrice structurée sous la forme J-tridiagonale par bloc. Nous proposons des algorithmes basés sur deux types de normalisation : la factorisation S R et la factorisation Rj R. Dans une dernière partie, nous proposons un algorithme qui généralise la méthode de Greville afin de déterminer la pseudo inverse de Moore-Penros bloc de lignes par bloc de lignes d'une matrice rectangulaire de manière itérative. Nous proposons un algorithme qui utilise la technique de bloc. Pour toutes ces méthodes, nous proposons des exemples numériques qui montrent l'efficacité de nos approches
We study, in this thesis, some numerical block Krylov subspace methods. These methods preserve geometric properties of the reduced matrix (Hamiltonian or skew-Hamiltonian or symplectic). Among these methods, we interest on block symplectic Arnoldi, namely block J-Arnoldi algorithm. Our main goal is to study this method, theoretically and numerically, on using ℝ²nx²s as free module on (ℝ²sx²s, +, x) with s ≪ n the size of block. A second aim is to study the approximation of exp (A)V, where A is a real Hamiltonian and skew-symmetric matrix of size 2n x 2n and V a rectangular matrix of size 2n x 2s on block Krylov subspace Km (A, V) = blockspan {V, AV,...Am-1V}, that preserve the structure of the initial matrix. this approximation is required in many applications. For example, this approximation is important for solving systems of ordinary differential equations (ODEs) or time-dependant partial differential equations (PDEs). We also present a block symplectic structure preserving Lanczos method, namely block J-Lanczos algorithm. Our approach is based on a block J-tridiagonalization procedure of a structured matrix. We propose algorithms based on two normalization methods : the SR factorization and the Rj R factorization. In the last part, we proposea generalized algorithm of Greville method for iteratively computing the Moore-Penrose inverse of a rectangular real matrix. our purpose is to give a block version of Greville's method. All methods are completed by many numerical examples
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Chen, Yu Chuan, and 陳又權. "Augmented Block Cimmino Distributed Algorithm for solving a tridiagonal Matrix on GPU." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/47971311649912636962.

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碩士
國立清華大學
資訊工程學系
103
The tridiagonal solver nowadays appears as a fundamental component in scientific and engi-neering problems, such as Alternating Direction Implicit methods (ADI), fluid Simulation, and Poisson’s equation. Due to the particular sparse format of tridiagonal matrix, many algorithms of solving the system are conceived. Previously, the main stream of solving the system is by using Diagonal Pivoting to reduce the accuracy issue. But, Diagonal Pivoting has its limits and will lead to error solution while the condition number increases. Augmented Block Cimmino Distributed (ABCD) algorithm serves as another option when trying to resolve the problem accurately. In this thesis, we study and implement the ABCD algorithm on GPU. Because of the spe-cial structure of tridiagonal matrices, we investigate the boundary padding technique to eliminate the execution branches on GPU for better performance. In addition, our implementation incorpo-rates various performance optimization techniques, such as memory coalesce, to further enhance the performance. In the experiments, we evaluate the accuracy and performance of our GPU im-plementation against CPU implementation, and analyze the effectiveness of each performance op-timization technique. The performance of GPU version is about 15 times faster than that of the CPU version.
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Books on the topic "Block tridiagonal matrix"

1

Blech, Richard A. Parallel Gaussian estimation of a block tridiagonal matrix using multiple microcomputers. Cleveland, Ohio: Lewis Research Center, 1989.

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2

Parallel Gaussian elimination of a block tridiagonal matrix using multiple microcomputers. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1989.

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Parallel Gaussian elimination of a block tridiagonal matrix using multiple microcomputers. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1989.

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Conference papers on the topic "Block tridiagonal matrix"

1

Iannelli, G. S., and A. J. Baker. "Accuracy and Efficiency Assessments for a Weak Statement CFD Algorithm for High-Speed Aerodynamics." In ASME 1992 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/92-gt-433.

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A bilinear finite element, implicit Runge-Kutta space-time discretization has been established for an aerodynamics weak statement CFD algorithm. The algorithm admits real-gas effects simulation, for reliable hypersonic flow characterization, via an equilibrium reacting air model. The terminal algebraic system is solved using an efficient block-tridiagonal quasi-Newton linear algebra procedure that employs tensor matrix product factorizations within a lexicographic mesh-sweeping protocol. A block solution-adaptive remeshing, for totally arbitrary convex elements, is also utilized to facilitate accurate shock and/or boundary layer flow resolution. Numerical validations are presented for representative benchmark supersonic-hypersonic aerodynamics problem statements.
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Zhang, Wei, and Timothy S. Fisher. "Simulation of Phonon Interfacial Transport in Strained Silicon-Germanium Heterostructures." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-80053.

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A nonequilibrium Green’s function (NEGF) method is used to simulate the phonon transport across a strained thin film between two semi-infinite contacts. The calculation of dynamical matrix, self-energy matrix and transmission function are discussed. Uncoupled Green’s functions are computed numerically using a block tridiagonal algorithm. The numerical role of the broadening constant is investigated. The bulk density of states in a single atomic chain is calculated and compares well with an analytical solution. The transmission function and thermal conductance across the thin film are evaluated for two different configurations (Ge-Si-Ge and Si-Ge-Si) and compared against homogeneous bulk systems (Si only and Ge only), indicating that heterogeneous interfaces reduce thermal conductance significantly.
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Journal articles
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