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Journal articles on the topic 'Block tridiagonal matrix'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

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 (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, t

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2

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 (2000): 103–25. http://dx.doi.org/10.1016/s0024-3795(00)00146-4.

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3

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 (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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4

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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5

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 (2010): 6392–404. http://dx.doi.org/10.1016/j.jcp.2010.04.049.

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6

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

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7

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 (2008): 3174–90. http://dx.doi.org/10.1016/j.jcp.2007.11.035.

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8

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 interpolatio

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9

Yun, Jae Heon. "Block incomplete factorization preconditioners for a symmetric block-tridiagonal M-matrix." Journal of Computational and Applied Mathematics 94, no. 2 (1998): 133–52. http://dx.doi.org/10.1016/s0377-0427(98)00078-8.

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10

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 (2007): 117–42. http://dx.doi.org/10.1137/050638230.

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11

Duan, Zhi Jian. "Parallel Algorithm for Solving Block-Tridiagonal Linear Systems." Applied Mechanics and Materials 427-429 (September 2013): 2420–23. http://dx.doi.org/10.4028/www.scientific.net/amm.427-429.2420.

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Efficient parallel iterative algorithm is investigated for solving block-tridiagonal linear systems on distributed-memory multi-computers. Based on Galerkin theory, the communication only need twice between the adjacent processors per iteration step. Furthermore, the condition for convergence is given when the coefficient matrix A is a symmetric positive definite matrix. Numerical experiments implemented on the cluster verify that our algorithm parallel acceleration rates and efficiency are higher than the multisplitting one, and has the advantages over the multisplitting method of high effici

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12

Takahira, S., T. Sogabe, and T. S. Usuda. "Bidiagonalization of (k, k + 1)-tridiagonal matrices." Special Matrices 7, no. 1 (2019): 20–26. http://dx.doi.org/10.1515/spma-2019-0002.

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Abstract In this paper,we present the bidiagonalization of n-by-n (k, k+1)-tridiagonal matriceswhen n < 2k. Moreover,we show that the determinant of an n-by-n (k, k+1)-tridiagonal matrix is the product of the diagonal elements and the eigenvalues of the matrix are the diagonal elements. This paper is related to the fast block diagonalization algorithm using the permutation matrix from [T. Sogabe and M. El-Mikkawy, Appl. Math. Comput., 218, (2011), 2740-2743] and [A. Ohashi, T. Sogabe, and T. S. Usuda, Int. J. Pure and App. Math., 106, (2016), 513-523].

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13

Reuter, Matthew G., and Judith C. Hill. "An efficient, block-by-block algorithm for inverting a block tridiagonal, nearly block Toeplitz matrix." Computational Science & Discovery 5, no. 1 (2012): 014009. http://dx.doi.org/10.1088/1749-4699/5/1/014009.

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14

Higham, Nicholas J. "Stability of block LDLT factorization of a symmetric tridiagonal matrix." Linear Algebra and its Applications 287, no. 1-3 (1999): 181–89. http://dx.doi.org/10.1016/s0024-3795(98)10074-5.

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15

BOWDEN, KEITH. "A DIRECT SOLUTION TO THE BLOCK TRIDIAGONAL MATRIX INVERSION PROBLEM." International Journal of General Systems 15, no. 3 (1989): 185–98. http://dx.doi.org/10.1080/03081078908935044.

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16

Coon, A. B., and M. A. Stadtherr. "Generalized block-tridiagonal matrix orderings for parallel computation in process flowsheeting." Computers & Chemical Engineering 19, no. 6-7 (1995): 787–805. http://dx.doi.org/10.1016/0098-1354(94)00081-6.

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17

Zhao, Jinxi, Weiguo Wang, and Weiqing Ren. "Stability of the Matrix Factorization for Solving Block Tridiagonal Symmetric Indefinite Linear Systems." BIT Numerical Mathematics 44, no. 1 (2004): 181–88. http://dx.doi.org/10.1023/b:bitn.0000025084.86306.0a.

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18

Bliadze, I. D., and G. V. Meladze. "Iterative decomposition methods for solving systems of equations with a block-tridiagonal matrix." USSR Computational Mathematics and Mathematical Physics 29, no. 3 (1989): 112–19. http://dx.doi.org/10.1016/0041-5553(89)90157-2.

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19

Iannelli, G. S., and A. J. Baker. "Accuracy and Efficiency Assessments for a Weak Statement CFD Algorithm for High-Speed Aerodynamics." Journal of Engineering for Gas Turbines and Power 116, no. 3 (1994): 468–73. http://dx.doi.org/10.1115/1.2906844.

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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 effect 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 a

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20

Godfrin, E. M. "A method to compute the inverse of an n-block tridiagonal quasi-Hermitian matrix." Journal of Physics: Condensed Matter 3, no. 40 (1991): 7843–48. http://dx.doi.org/10.1088/0953-8984/3/40/005.

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21

Ivanov, M. A. "An economic algorithm for solving systems of difference equations with a block-tridiagonal matrix." USSR Computational Mathematics and Mathematical Physics 26, no. 2 (1986): 84–86. http://dx.doi.org/10.1016/0041-5553(86)90013-3.

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22

Lai, Jiangzhou, and Linzhang Lu. "Real Fast Structure-Preserving Algorithm for Eigenproblem of Complex Hermitian Matrices." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/438320.

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It is well known that the flops for complex operations are usually 4 times of real cases. In the paper, using real operations instead of complex, a real fast structure-preserving algorithm for eigenproblem of complex Hermitian matrices is given. We make use of the real symmetric and skew-Hamiltonian structure transformed by Wilkinson's way, focus on symplectic orthogonal similarity transformations and their structure-preserving property, and then reduce it into a two-by-two block tridiagonal symmetric matrix. Finally a real algorithm can be quickly obtained for eigenvalue problems of the origi

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23

Ratnieks, Aloizs, and Marina Uhanova. "Application Of The Interlaced Sweep Method For The Solution Of Problems In Field Theory." Environment. Technology. Resources. Proceedings of the International Scientific and Practical Conference 3 (June 16, 2015): 170. http://dx.doi.org/10.17770/etr2015vol3.190.

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<p class="R-AbstractKeywords"><span lang="EN-US">For solution of problems in field theory the method of sweep is very popular. The authors suggest a very effective method of interlaced sweep. The essence of the interlaced sweep method lies in the fact that matrix of the linear algebraic equations system is broken into parts and the solution of separate blocks is sought by direct methods. Usually for each line of the grid a separate block is created. The system of block equations has a tridiagonal matrix where only elements of the main diagonal and two neighboring diagonals are diff

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24

Barfoot, Timothy D., James R. Forbes, and David J. Yoon. "Exactly sparse Gaussian variational inference with application to derivative-free batch nonlinear state estimation." International Journal of Robotics Research 39, no. 13 (2020): 1473–502. http://dx.doi.org/10.1177/0278364920937608.

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We present a Gaussian variational inference (GVI) technique that can be applied to large-scale nonlinear batch state estimation problems. The main contribution is to show how to fit both the mean and (inverse) covariance of a Gaussian to the posterior efficiently, by exploiting factorization of the joint likelihood of the state and data, as is common in practical problems. This is different than maximum a posteriori (MAP) estimation, which seeks the point estimate for the state that maximizes the posterior (i.e., the mode). The proposed exactly sparse Gaussian variational inference (ESGVI) tec

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25

Deng, Quanling. "Analytical solutions to some generalized and polynomial eigenvalue problems." Special Matrices 9, no. 1 (2021): 240–56. http://dx.doi.org/10.1515/spma-2020-0135.

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Abstract It is well-known that the finite difference discretization of the Laplacian eigenvalue problem −Δu = λu leads to a matrix eigenvalue problem (EVP) Ax =λx where the matrix A is Toeplitz-plus-Hankel. Analytical solutions to tridiagonal matrices with various boundary conditions are given in a recent work of Strang and MacNamara. We generalize the results and develop analytical solutions to certain generalized matrix eigenvalue problems (GEVPs) Ax = λBx which arise from the finite element method (FEM) and isogeometric analysis (IGA). The FEM matrices are corner-overlapped block-diagonal w

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26

Magdalena, Ikha, and Novry Erwina. "An Efficient Two-Layer Non-Hydrostatic Model for Investigating Wave Run-Up Phenomena." Computation 8, no. 1 (2019): 1. http://dx.doi.org/10.3390/computation8010001.

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In this paper, we study the maximum run-up of solitary waves on a sloping beach and over a reef through a non-hydrostatic model. We do a modification on the non-hydrostatic model derived by Stelling and Zijlema. The model is approximated by resolving the vertical fluid depth into two-layer system. In contrast to the two-layer model proposed by Stelling, here, we have a block of a tridiagonal matrix for the hydrodynamic pressure. The equations are then solved by applying a staggered finite volume method with predictor-corrector step. For validation, several test cases are presented. The first t

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27

Rafique, Anwar, Misiran, et al. "Hydromagnetic Flow of Micropolar Nanofluid." Symmetry 12, no. 2 (2020): 251. http://dx.doi.org/10.3390/sym12020251.

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Similar to other fluids (Newtonian and non-Newtonian), micropolar fluid also exhibits symmetric flow and exact symmetric solution similar to the Navier–Stokes equation; however, it is not always realizable. In this article, the Buongiorno mathematical model of hydromagnetic micropolar nanofluid is considered. A joint phenomenon of heat and mass transfer is studied in this work. This model indeed incorporates two important effects, namely, the Brownian motion and the thermophoretic. In addition, the effects of magnetohydrodynamic (MHD) and chemical reaction are considered. The fluid is taken ov

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28

BOLSTAD, JOHN H. "FOLLOWING PATHS OF SYMMETRY-BREAKING BIFURCATION POINTS." International Journal of Bifurcation and Chaos 02, no. 03 (1992): 559–76. http://dx.doi.org/10.1142/s0218127492000707.

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We propose a pseudo-arclength continuation algorithm for computing paths of Z 2-symmetry-breaking bifurcation points for two-parameter nonlinear elliptic problems. The algorithm consists of an Euler predictor step and a solution step composed of a sequence of Newton iterations. This work generalizes the algorithm of Werner and Spence for locating a one-parameter symmetry-breaking bifurcation point by using the approach of Keller and Fier for following a (two-parameter) path of limit points (a "fold"). By repeated use of the bordering algorithm, we solve linear systems whose matrix is the "symm

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29

Mateescu, D., M. P. Paidoussis, and W. G. Sim. "Three-Dimensional Viscous Flows Between Concentric Cylinders Executing Axially Variable Oscillations: A Hybrid Spectral/Finite Difference Solution." Journal of Applied Mechanics 62, no. 3 (1995): 667–73. http://dx.doi.org/10.1115/1.2895998.

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A hybrid spectral/finite difference method is developed in this paper for the analysis of three-dimensional unsteady viscous flows between concentric cylinders subjected to fully developed laminar flow and executing transverse oscillations. This method uses a partial spectral collocation approach, based on spectral expansions of the flow parameters in the transverse coordinates and time, in conjunction with a finite difference discretization of the axial derivatives. The finite difference discretization uses central differencing for the diffusion derivatives and a mixed central-upwind differen

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30

Koshy, Ranjana, and Ausif Mahmood. "Optimizing Deep CNN Architectures for Face Liveness Detection." Entropy 21, no. 4 (2019): 423. http://dx.doi.org/10.3390/e21040423.

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Face recognition is a popular and efficient form of biometric authentication used in many software applications. One drawback of this technique is that it is prone to face spoofing attacks, where an impostor can gain access to the system by presenting a photograph of a valid user to the sensor. Thus, face liveness detection is a necessary step before granting authentication to the user. In this paper, we have developed deep architectures for face liveness detection that use a combination of texture analysis and a convolutional neural network (CNN) to classify the captured image as real or fake

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31

Kudryavtsev, Oleg. "Finite Difference Methods for Option Pricing under Lévy Processes: Wiener-Hopf Factorization Approach." Scientific World Journal 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/963625.

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In the paper, we consider the problem of pricing options in wide classes of Lévy processes. We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation. The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps. The method is applicable for pricing barrier and American options. The pricing problem is reduced to the sequence of linear algebraic systems with a dense Toeplitz matrix; then the Wiener-Hopf factorization method is a

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32

Юлдашев, А. В., Н. В. Репин, and В. В. Спеле. "A parallel preconditioner based on the approximation of an inverse matrix by power series for solving sparse linear systems on graphics processors." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 4 (September 10, 2019): 444–56. http://dx.doi.org/10.26089/nummet.v20r439.

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Рассмотрена применимость метода AIPS, аппроксимирующего обратную матрицу на основе степенного разложения в ряд Неймана, в рамках двухступенчатого предобусловливателя CPR. Предложен ориентированный на архитектуру CUDA параллельный алгоритм решения линейных систем с трехдиагональной матрицей, состоящей из независимых блоков различного размера. Показано, что реализация предложенного алгоритма может более чем в 2 раза превосходить по быстродействию функции решения трехдиагональных систем из библиотеки cuSPARSE. Проведено тестирование метода BiCGStab с предобусловливателем CPRAIPS на современных GP

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33

"Integration of Compressive Sensing and Clustering in Wireless Sensor Networks using Block Tridiagonal Matrix Method." International Journal of Engineering and Advanced Technology 8, no. 6S2 (2019): 901–6. http://dx.doi.org/10.35940/ijeat.f1220.0886s219.

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The most dominant applications of wireless sensor networks (WSNs) is Environmental monitoring, it generally needs long time to operate. Although, the energy of inherent restriction has the bottle neck in scale of each WSN applications. This articler demonstrates the framework for an integration of compressive sensing and blocks tri-diagonal matrices (BDMs) for the clustering in WSNs that can be used as the matrices of measurement by the combination of data prediction that is involved with the compression and retrieval to achieve data processing precision and effectiveness in clustered WSNs sim

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