Relevant bibliographies by topics / Diagonally dominant linear systems

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Academic literature on the topic 'Diagonally dominant linear systems'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Diagonally dominant linear systems"

1

Huang, Rong, Jianzhou Liu, and Li Zhu. "Accurate solutions of diagonally dominant tridiagonal linear systems." BIT Numerical Mathematics 54, no. 3 (2014): 711–27. http://dx.doi.org/10.1007/s10543-014-0481-5.

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2

Zhang, Cheng-yi, Dan Ye, Cong-Lei Zhong, and SHUANGHUA SHUANGHUA. "Convergence on Gauss-Seidel iterative methods for linear systems with general H-matrices." Electronic Journal of Linear Algebra 30 (February 8, 2015): 843–70. http://dx.doi.org/10.13001/1081-3810.1972.

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It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible H−matrices (generalized strictly diagonally dominant matrices) and Hermitian positive definite matrices. But, the same is not necessarily true for linear systems with non-strictly diagonally dominant matrices and general H−matrices. This paper firstly proposes some necessary and sufficient conditions for convergence on Gauss-Seidel iterative methods to establish several new theoretical results on linear systems with nonstrictly diagonally dominant matrices and general H−matrices. Then, the convergence results on preconditioned Gauss-Seidel (PGS) iterative methods for general H−matrices are presented. Finally, some numerical examples are given to demonstrate the results obtained in this paper.
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3

Doan, T. S., and S. Siegmund. "Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays." Abstract and Applied Analysis 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/210156.

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We introduce a notion of attractivity for delay equations which are defined on bounded time intervals. Our main result shows that linear delay equations are finite-time attractive, provided that the delay is only in the coupling terms between different components, and the system is diagonally dominant. We apply this result to a nonlinear Lotka-Volterra system and show that the delay is harmless and does not destroy finite-time attractivity.
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4

Shahruz, S. M., and F. Ma. "Approximate Decoupling of the Equations of Motion of Linear Underdamped Systems." Journal of Applied Mechanics 55, no. 3 (1988): 716–20. http://dx.doi.org/10.1115/1.3125855.

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One common procedure in the solution of a normalized damped linear system with small off-diagonal damping elements is to replace the normalized damping matrix by a selected diagonal matrix. The extent of approximation introduced by this method of decoupling the system is evaluated, and tight error bounds are derived. Moreover, if the normalized damping matrix is diagonally dominant, it is shown that decoupling the system by neglecting the off-diagonal elements indeed minimizes the error bound.
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5

Frommer, A., та G. Mayer. "Linear systems with Ω-diagonally dominant matrices and related ones". Linear Algebra and its Applications 186 (червень 1993): 165–81. http://dx.doi.org/10.1016/0024-3795(93)90289-z.

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6

Siahlooei, Esmaeil, and Seyed Abolfazl Shahzadeh Fazeli. "Two Iterative Methods for Solving Linear Interval Systems." Applied Computational Intelligence and Soft Computing 2018 (October 8, 2018): 1–13. http://dx.doi.org/10.1155/2018/2797038.

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Conjugate gradient is an iterative method that solves a linear system Ax=b, where A is a positive definite matrix. We present this new iterative method for solving linear interval systems Ãx̃=b̃, where à is a diagonally dominant interval matrix, as defined in this paper. Our method is based on conjugate gradient algorithm in the context view of interval numbers. Numerical experiments show that the new interval modified conjugate gradient method minimizes the norm of the difference of Ãx̃ and b̃ at every step while the norm is sufficiently small. In addition, we present another iterative method that solves Ãx̃=b̃, where à is a diagonally dominant interval matrix. This method, using the idea of steepest descent, finds exact solution x̃ for linear interval systems, where Ãx̃=b̃; we present a proof that indicates that this iterative method is convergent. Also, our numerical experiments illustrate the efficiency of the proposed methods.
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7

Spielman, Daniel A., and Shang-Hua Teng. "Nearly Linear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems." SIAM Journal on Matrix Analysis and Applications 35, no. 3 (2014): 835–85. http://dx.doi.org/10.1137/090771430.

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8

Wang, Guangbin, Hao Wen, and Ting Wang. "Convergence of GAOR Iterative Method with Strictly Diagonally Dominant Matrices." Journal of Applied Mathematics 2011 (2011): 1–10. http://dx.doi.org/10.1155/2011/713795.

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We discuss the convergence of GAOR method for linear systems with strictly diagonally dominant matrices. Moreover, we show that our results are better than ones of Darvishi and Hessari (2006), Tian et al. (2008) by using three numerical examples.
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9

Belhaj, Skander, Fahd Hcini, Maher Moakher, and Yulin Zhang. "A fast algorithm for solving diagonally dominant symmetric quasi-pentadiagonal Toeplitz linear systems." Journal of Mathematical Chemistry 59, no. 3 (2021): 757–74. http://dx.doi.org/10.1007/s10910-021-01217-7.

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10

Tian, Gui-Xian, Ting-Zhu Huang, and Shu-Yu Cui. "Convergence of generalized AOR iterative method for linear systems with strictly diagonally dominant matrices." Journal of Computational and Applied Mathematics 213, no. 1 (2008): 240–47. http://dx.doi.org/10.1016/j.cam.2007.01.016.

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