Relevant bibliographies by topics / Diagonally dominant linear systems

Academic literature on the topic 'Diagonally dominant linear systems'

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Published: 6 September 2023

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Journal articles on the topic "Diagonally dominant linear systems"

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Huang, Rong, Jianzhou Liu, and Li Zhu. "Accurate solutions of diagonally dominant tridiagonal linear systems." BIT Numerical Mathematics 54, no. 3 (March 18, 2014): 711–27. http://dx.doi.org/10.1007/s10543-014-0481-5.

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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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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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Shahruz, S. M., and F. Ma. "Approximate Decoupling of the Equations of Motion of Linear Underdamped Systems." Journal of Applied Mechanics 55, no. 3 (September 1, 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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Frommer, A., and G. Mayer. "Linear systems with Ω-diagonally dominant matrices and related ones." Linear Algebra and its Applications 186 (June 1993): 165–81. http://dx.doi.org/10.1016/0024-3795(93)90289-z.

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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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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 (January 2014): 835–85. http://dx.doi.org/10.1137/090771430.

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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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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 (February 2, 2021): 757–74. http://dx.doi.org/10.1007/s10910-021-01217-7.

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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 (March 2008): 240–47. http://dx.doi.org/10.1016/j.cam.2007.01.016.

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Dissertations / Theses on the topic "Diagonally dominant linear systems"

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Macintosh, Hamish J. "Solving diagonally dominant tridiagonal linear systems with FPGAs in an heterogeneous computing environment." Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/130762/1/Hamish_Macintosh_Thesis.pdf.

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The primary motivation for this research is to determine the feasibility of targeting FPGAs for use in accelerating general purpose scientific computing on heterogeneous computing platforms. This has been explored through the lens of a common scientific computing problem, solving a diagonally dominant tridiagonal linear system. With this focus, a comparative analysis of solver implementations for FPGA, GPU, CPU and heterogeneous combinations thereof has been completed using OpenCL as a common programming framework.
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Kamra, Rabia. "Parallel computation of diagonally dominant linear systems." Thesis, 2017. http://localhost:8080/xmlui/handle/12345678/7431.

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Book chapters on the topic "Diagonally dominant linear systems"

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Mikkelsen, Carl Christian Kjelgaard, and Bo Kågström. "Parallel Solution of Narrow Banded Diagonally Dominant Linear Systems." In Applied Parallel and Scientific Computing, 280–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28145-7_28.

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Kjelgaard Mikkelsen, Carl Christian, and Bo Kågström. "Incomplete Cyclic Reduction of Banded and Strictly Diagonally Dominant Linear Systems." In Parallel Processing and Applied Mathematics, 80–91. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31464-3_9.

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Arbenz, Peter. "On experiments with a parallel direct solver for diagonally dominant banded linear systems." In Lecture Notes in Computer Science, 11–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0024679.

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Arbenz, Peter, Andrew Cleary, Jack Dongarra, and Markus Hegland. "A Comparison of Parallel Solvers for Diagonally Dominant and General Narrow-Banded Linear Systems II." In Euro-Par’99 Parallel Processing, 1078–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-48311-x_151.

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Lyche, Tom. "Diagonally Dominant Tridiagonal Matrices; Three Examples." In Numerical Linear Algebra and Matrix Factorizations, 27–55. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36468-7_2.

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Mikkelsen, Carl Christian Kjelgaard, and Bo Kågström. "Approximate Incomplete Cyclic Reduction for Systems Which Are Tridiagonal and Strictly Diagonally Dominant by Rows." In Applied Parallel and Scientific Computing, 250–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36803-5_18.

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PAARDEKOOPER, M. H. C. "A quadratically convergent parallel Jacobi process for diagonally dominant matrices with distinct eigenvalues* *This research is part of the VF-program “Parallelle Algoritmiek”, THD-WI-08185-25, which has been approved by the Netherlands Ministery of Education and Sciences." In Parallel Algorithms for Numerical Linear Algebra, 3–16. Elsevier, 1990. http://dx.doi.org/10.1016/b978-0-444-88621-7.50006-2.

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Krukier, B. L. "Product triangular iterative method for solution of linear equation systems with dominant skew-symmetric part." In Computational Fluid and Solid Mechanics 2003, 2031–34. Elsevier, 2003. http://dx.doi.org/10.1016/b978-008044046-0.50498-x.

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Burgess, Kevin. "Feral Systems in Enterprise Resource Planning Systems." In Feral Information Systems Development, 242–65. IGI Global, 2014. http://dx.doi.org/10.4018/978-1-4666-5027-5.ch012.

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In order to gain deeper insights into the causal factors associated with feral systems, it is necessary to first understand how the underlying, and often unchallenged, assumptions of current theories shape, influence, and ultimately limit our understanding of these phenomena. A meta-theoretical analysis is presented to make more explicit the foundational assumptions guiding much of the current literature and demonstrating the various limitations associated with these assumptions. The implications of these limitations for theory development are then examined. The main conclusion drawn is that the dominant discourse in the ERPS literature has used overly simplified concepts to understand complex phenomena like feral systems, which are open, non-linear, context-sensitive, and value-driven. The efforts of scholars would be more effective if directed to a clearer appreciation of the present limitations on how feral systems are understood rather than simply conducting more research using the same approaches that have dominated to date.
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Thomas, Michael E. "Optical Propagation in Gases and the Atmosphere of the Earth." In Optical Propagation in Linear Media. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780195091618.003.0012.

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Propagation within the atmosphere is an important consideration concerning the performance of many electro-optical systems. An electro-optical system can be described as containing three basic components: source, detector, and propagation medium. Because of the quality of source and detection systems today, often the limiting factor in overall system performance is the propagation medium. Thus a thorough discussion of the atmosphere and various mechanisms of attenuation is required. Absorption, scattering, and turbulence are the dominant mechanisms of signal loss and distortion. This chapter covers gaseous absorption and scattering in the atmosphere of the earth. Turbulence is not covered, and the reader is referred to other texts (see Chapter 1, Refs. 1.10 and 1.11). The atmosphere surrounds and protects the earth in the form of a gaseous blanket that acts as the transition between the solid surface of the earth and the near-vacuum of the outer solar atmosphere. It acts as a shield against harmful particle radiation, meteors, and high-energy photons. The dynamics of the atmosphere drive the weather on the surface. It provides for life itself as part of the earth’s biosphere. Thus optical propagation in this medium has many important characteristics and consequences. These include meteorological optics, infrared and visible astronomy, remote sensing, and electro-optical systems performance in general. Therefore, it is appropriate to begin this chapter with an introduction to the nature of the atmosphere. The atmosphere is composed of gases and suspended particles or aerosols at various temperatures and concentrations as a function of altitude and azimuth. The variations in altitude show a marked structure. Six main horizontal layers form the stratified structure of the atmosphere, as shown in Fig. 7.1. The lowest is the troposphere, which extends from ground level to approximately 11 km (36,000 ft or 7 mi.). The temperature in this layer generally decreases with increasing altitude at the rate of 6.5 K/km. However, variations can exist on this rate, which creates interesting refractive effects. The pressure varies from one atmosphere at sea level to a few tenths of an atmosphere at the top of this layer.
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Conference papers on the topic "Diagonally dominant linear systems"

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Morzfeld, Matthias, Nopdanai Ajavakom, and Fai Ma. "Some Remarks About the Decoupling Approximation of Damped Linear Systems." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86319.

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A common approximation in the analysis of non-classically damped systems is to ignore the off-diagonal elements of the modal damping matrix. This procedure is termed the decoupling approximation. It is generally believed that errors due to the decoupling approximation should be negligible if the modal damping matrix is diagonally dominant. In addition, the errors are expected to decrease as the modal damping matrix becomes more diagonally dominant. It is shown numerically in this paper that, over a finite range, errors due to the decoupling approximation can increase monotonically at any specified rate while the modal damping matrix becomes more diagonally dominant with its off-diagonal elements decreasing continuously in magnitude. These unexpected drifts in errors due to the decoupling approximation can be observed at any driving frequency. Small off-diagonal elements in the modal damping matrix may not be sufficient to ensure small errors due to the decoupling approximation. Error-criteria based solely upon diagonal dominance of the modal damping matrix cannot be accurate.
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Rao, S. Chandra Sekhara, and Rabia Kamra. "A Stable Parallel Algorithm for Diagonally Dominant Tridiagonal Linear Systems." In 2015 IEEE 22nd International Conference on High Performance Computing (HiPC). IEEE, 2015. http://dx.doi.org/10.1109/hipc.2015.31.

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Morzfeld, Matthias, Nopdanai Ajavakom, and Fai Ma. "Diagonal Dominance and the Decoupling Approximation in Damped Discrete Linear Systems." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35690.

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The principal coordinates of a non-classically damped linear system are coupled by nonzero off-diagonal element of the modal damping matrix. In the analysis of non-classically damped systems, a common approximation is to ignore the off-diagonal elements of the modal damping matrix. This procedure is termed the decoupling approximation. It is widely accepted that if the modal damping matrix is diagonally dominant, then errors due to the decoupling approximation must be small. In addition, it is intuitively believed that the more diagonal the modal damping matrix, the less will be the errors in the decoupling approximation. Two quantitative measures are proposed in this paper to measure the degree of being diagonal dominant in modal damping matrices. It is demonstrated that, over a finite range, errors in the decoupling approximation can continuously increase while the modal damping matrix becomes more and more diagonal with its off-diagonal elements decreasing in magnitude continuously. An explanation for this unexpected behavior is presented. Within a practical range of engineering applications, diagonal dominance of the modal damping matrix may not be sufficient for neglecting modal coupling in a damped system.
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Rao, S. Chandra Sekhara, and Rabia Kamra. "A computational technique for parallel solution of diagonally dominant banded linear systems." In 2021 IEEE 28th International Conference on High Performance Computing, Data, and Analytics (HiPC). IEEE, 2021. http://dx.doi.org/10.1109/hipc53243.2021.00064.

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Marrakchi, Sirine, and Heni Kaaniche. "Solving Band Diagonally Dominant Linear Systems Using Gaussian Elimination: Shared-Memory Parallel Programming with OpenMP." In 2023 IEEE Symposium on Computers and Communications (ISCC). IEEE, 2023. http://dx.doi.org/10.1109/iscc58397.2023.10218238.

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Ma, F., and J. H. Hwang. "Approximate Solution of Nonclassically Damped Systems." In ASME 1991 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/cie1991-0117.

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Abstract In analyzing a nonclassically damped linear system, one common procedure is to neglect those damping terms which are nonclassical, and retain the classical ones. This approach is termed the method of approximate decoupling. For large-scale systems, the computational effort at adopting approximate decoupling is at least an order of magnitude smaller than the method of complex modes. In this paper, the error introduced by approximate decoupling is evaluated. A tight error bound, which can be computed with relative ease, is given for this method of approximate solution. The role that modal coupling plays in the control of error is clarified. If the normalized damping matrix is strongly diagonally dominant, it is shown that adequate frequency separation is not necessary to ensure small errors.
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Xue-Bo Chen and Wei Wang. "Block Diagonally Dominant Decomposition for Large Scale Systems." In 4th International Conference on Control and Automation. Final Program and Book of Abstracts. IEEE, 2003. http://dx.doi.org/10.1109/icca.2003.1595083.

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Wang, Cheng, and Huanbin Liu. "Stability of Generalized Diagonally Dominant Fuzzy Dynamical Systems." In 2009 Sixth International Conference on Fuzzy Systems and Knowledge Discovery. IEEE, 2009. http://dx.doi.org/10.1109/fskd.2009.580.

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Xie, Wei-Chau. "Localization of Vibration Propagation in Randomly Disordered Weakly Coupled Two-Dimensional Cantilever-Spring Arrays." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-0571.

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Abstract In this paper, the method of regular perturbation for a linear algebraic system is applied to study localization of vibration propagation in randomly disordered weakly coupled two-dimensional cantilever-spring arrays under external harmonic excitations. Iterative equations are obtained to express the displacement vector of the cantilevers on the Mth “layer” in the Mth-order perturbation in terms of those on the (M − 1)th “layer” in the (M − 1)th-order perturbation. Localization factors, which characterize the average exponential rates of decay of the amplitudes of vibration, are defined in terms of the angles of orientation. First-order approximate results of the localization factors are obtained using a combined analytical-numerical approach. The localization factors are symmetric about the horizontal and vertical axes passing through the cantilever that is being externally excited. For the systems under consideration, the direction in which vibration is dominant corresponds to the smallest localization factor; whereas the “diagonal” directions correspond to the largest localization factor.
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Pfifer, Harald, and Tamas Peni. "Model reduction for linear parameter varying systems using scaled diagonal dominance." In 2016 American Control Conference (ACC). IEEE, 2016. http://dx.doi.org/10.1109/acc.2016.7525344.

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