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Relevant bibliographies by topics / Gauss-Seidel

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Academic literature on the topic 'Gauss-Seidel'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 June 2025

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Journal articles on the topic "Gauss-Seidel"

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Tuljaram Meghwar, Sher khan Awan, Muhammad Tariq, Muhammad Suleman, and Asif Ali Shaikh. "Substitutional Based Gauss-Seidel Method For Solving System of Linear Algebraic Equations." Babylonian Journal of Mathematics 2024 (January 10, 2024): 1–12. http://dx.doi.org/10.58496/bjm/2024/001.

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In this research paper a new modification of Gauss-Seidel method has been presented for solving the system of linear algebraic equations. The systems of linear algebraic equations have an important role in the field of science and engineering. This modification has been developed by using the procedure of Gauss-Seidel method and the concept of substitution techniques. Developed modification of Gauss-Seidel method is a fast convergent as compared to Gauss Jacobi’s method, Gauss-Seidel method and successive over-relaxation (SOR) method. It works on the diagonally dominant as well as positive definite symmetric systems of linear algebraic equations. Its solution has been compared with the Gauss Jacobi’s method, Gauss-Seidel method and Successive over-Relaxation method by taking different systems of linear algebraic equations and found that, it was reducing to the number of iterations and errors in each problem.

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SEBRO, AMRACH, HAILU MULETA, and SOLOMON GEBREGIORGIS. "Extrapolated refinement of generalized gauss- seidel scheme for solving system of linear equations." Berhan International Research Journal of Science and Humanities 4 (March 22, 2020): 12–23. http://dx.doi.org/10.61593/dbu.birjsh.01.01.55.

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In this paper, Extrapolated Refinement of Generalized Gauss-Seidel scheme for solving system of linear equations has been presented. In order to accelerate the rate of convergence of the scheme, the one-parameter family of splitting procedure has been introduced and the convergence of the method is well established. To validate the proposed method, three numerical examples were considered. Comparisons were made among Refinement of Generalized Jacobi, Generalized Gauss-Seidel, Refinement of Generalized Gauss-Seidel and Extrapolated Refinement of Generalized Gauss-Seidel schemes with respect to the number of iterations to converge, computational running time and storage capacity. The numerical results presented in tables show that the Extrapolated Refinement of Generalized Gauss-Seidel scheme is more efficient than the other three schemes considered for comparison.

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Enyew, Tesfaye Kebede, Gurju Awgichew, Eshetu Haile, and Gashaye Dessalew Abie. "Second-refinement of Gauss-Seidel iterative method for solving linear system of equations." Ethiopian Journal of Science and Technology 13, no. 1 (2020): 1–15. http://dx.doi.org/10.4314/ejst.v13i1.1.

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Although large and sparse linear systems can be solved using iterative methods, its number of iterations is relatively large. In this case, we need to modify the existing methods in order to get approximate solutions in a small number of iterations. In this paper, the modified method called second-refinement of Gauss-Seidel method for solving linear system of equations is proposed. The main aim of this study was to minimize the number of iterations, spectral radius and to increase rate of convergence. The method can also be used to solve differential equations where the problem is transformed to system of linear equations with coefficient matrices that are strictly diagonally dominant matrices, symmetric positive definite matrices or M-matrices by using finite difference method. As we have seen in theorem 1and we assured that, if A is strictly diagonally dominant matrix, then the modified method converges to the exact solution. Similarly, in theorem 2 and 3 we proved that, if the coefficient matrices are symmetric positive definite or M-matrices, then the modified method converges. And moreover in theorem 4 we observed that, the convergence of second-refinement of Gauss-Seidel method is faster than Gauss-Seidel and refinement of Gauss-Seidel methods. As indicated in the examples, we demonstrated the efficiency of second-refinement of Gauss-Seidel method better than Gauss-Seidel and refinement of Gauss-Seidel methods.

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Vinsensia, Desi, Yulia Utami, Fathia Siregar, and Muhammad Arifin. "Improve refinement approach iterative method for solution linear equition of sparse matrices." Jurnal Teknik Informatika C.I.T Medicom 15, no. 6 (2024): 306–13. http://dx.doi.org/10.35335/cit.vol15.2024.721.pp306-313.

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In this paper, systems of linear equations on sparse matrices investigated through modified improve method using Gauss-Seidel and successive overrelaxation (SOR) approach. Taking into adapted convergence rate on the Improve refinement Gauss-seidel outperformed the prior two Gauss-Seidel methods in terms of rate of convergence and number of iterations required to solve the problem by applying a modified version of the Gauss-Seidel approach. to observe the effectiveness of this method, the numerical example is given. The main findings in this study, that Gauss seidel improvement refinement gives optimum spectral radius and convergence rate. Similarly, the SOR improved refinement method gives. Considering their performance, using parameters such as time to converge, number of iterations required to converge and spectral radius level of accuracy. However, SOR works with relaxation values so that it greatly affects the convergence rate and spectral radius results if given greater than 1.

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Alvarez, Gustavo Benitez, Diomar Cesar Lobão, and Welton Alves de Menezes. "The m-order Jacobi, Gauss–Seidel and symmetric Gauss–Seidel methods." Pesquisa e Ensino em Ciências Exatas e da Natureza 6 (March 28, 2022): 1773. http://dx.doi.org/10.29215/pecen.v6i0.1773.

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<p>Aqui, são desenvolvidos métodos de ordem m que conservam a forma dos métodos de primeira<br />ordem. Métodos de ordem m têm uma taxa de convergência maior que sua versão de primeira ordem.<br />Esses métodos de ordem m são subsequências de seu método precursor, onde alguns benefícios do uso<br />de processadores vetoriais e paralelos podem ser explorados. Os resultados numéricos obtidos com as<br />implementações vetoriais mostram vantagens computacionais quando comparadas as versões de<br />primeira ordem.</p>

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Duan, Ban Xiang, Wen Ying Zeng, and Xiao Ping Zhu. "A Preconditioned Gauss-Seidel Iterative Method for Linear Complementarity Problem in Intelligent Materials System." Advanced Materials Research 340 (September 2011): 3–8. http://dx.doi.org/10.4028/www.scientific.net/amr.340.3.

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In this paper, the authors first set up new preconditioned Gauss-Seidel iterative method for solving the linear complementarity problem, whose preconditioned matrix is introduced. Then certain elementary operations row are performed on system matrix before applying the Gauss-Seidel iterative method. Moreover the sufficient conditions for guaranteeing the convergence of the new preconditioned Gauss-Seidel iterative method are presented. Lastly we report some computational results with the proposed method.

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Chafik, Sanaa, Abdelhadi Larach, and Cherki Daoui. "Parallel Hierarchical Pre-Gauss-Seidel Value Iteration Algorithm." International Journal of Decision Support System Technology 10, no. 2 (2018): 1–22. http://dx.doi.org/10.4018/ijdsst.2018040101.

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The standard Value Iteration (VI) algorithm, referred to as Value Iteration Pre-Jacobi (PJ-VI) algorithm, is the simplest Value Iteration scheme, and the well-known algorithm for solving Markov Decision Processes (MDPs). In the literature, several versions of VI algorithm were developed in order to reduce the number of iterations: the VI Jacobi (VI-J) algorithm, the Value Iteration Pre-Gauss-Seidel (VI-PGS) algorithm and the VI Gauss-Seidel (VI-GS) algorithm. In this article, the authors combine the advantages of VI Pre Gauss-Seidel algorithm, the decomposition technique and the parallelism in order to propose a new Parallel Hierarchical VI Pre-Gauss-Seidel algorithm. Experimental results show that their approach performs better than the traditional VI schemes in the case where the global problem can be decomposed into smaller problems.

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Ko, Ren-Song, Po-Liang Lin, and Pei-Yu Chiang. "Gauss-seidel correction algorithm." ACM Transactions on Sensor Networks 10, no. 1 (2013): 1–42. http://dx.doi.org/10.1145/2529190.

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Nirupma Bhatti and Niketa. "Comparative study of Symmetric Gauss-Seidel methods and preconditioned Symmetric Gauss-Seidel methods for linear system." International Journal of Science and Research Archive 8, no. 1 (2023): 940–47. http://dx.doi.org/10.30574/ijsra.2023.8.1.0155.

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This paper deals with the comparative study of preconditioned Symmetric Gauss-Seidel (SGS), New Symmetric Gauss-Seidel (NSGS), and Parametric Symmetric Gauss-Seidel (PSGS) methods for solving the linear system Ax = b are considered. This system is preconditioned with precondition type I + S. Convergence properties are analyzed with standard procedures and a numerical experiment is undertaken to compare the efficiency of the matrix. Algorithms are prepared. MATLAB software is used for checking computational efficiency of preconditioned iterative methods. Results indicate the effectiveness of preconditioning.

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Saqib, Muhammad, Muhammad Akram, and Shahida Bashir. "Certain efficient iterative methods for bipolar fuzzy system of linear equations." Journal of Intelligent & Fuzzy Systems 39, no. 3 (2020): 3971–85. http://dx.doi.org/10.3233/jifs-200084.

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A bipolar fuzzy set model is an extension of fuzzy set model. We develop new iterative methods: generalized Jacobi, generalized Gauss-Seidel, refined Jacobi, refined Gauss-seidel, refined generalized Jacobi and refined generalized Gauss-seidel methods, for solving bipolar fuzzy system of linear equations(BFSLEs). We decompose n × n BFSLEs into 4n × 4n symmetric crisp linear system. We present some results that give the convergence of proposed iterative methods. We solve some BFSLEs to check the validity, efficiency and stability of our proposed iterative schemes. Further, we compute Hausdorff distance between the exact solutions and approximate solution of our proposed schemes. The numerical examples show that some proposed methods converge for the BFSLEs, but Jacobi and Gauss-seidel iterative methods diverge for BFSLEs. Finally, comparison tables show the performance, validity and efficiency of our proposed iterative methods for BFSLEs.

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Dissertations / Theses on the topic "Gauss-Seidel"

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Simonis, Joseph P. "Newton-Picard Gauss-Seidel." Link to electronic thesis, 2004. http://www.wpi.edu/Pubs/ETD/Available/etd-051305-162036/unrestricted/simonis.pdf.

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Simonis, Joseph P. "Newton-Picard Gauss-Seidel." Digital WPI, 2005. https://digitalcommons.wpi.edu/etd-dissertations/285.

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Newton-Picard methods are iterative methods that work well for computing roots of nonlinear equations within a continuation framework. This project presents one of these methods and includes the results of a computation involving the Brusselator problem performed by an implementation of the method. This work was done in collaboration with Andrew Salinger at Sandia National Laboratories.

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Wu, Wei. "Paving the Randomized Gauss-Seidel." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/scripps_theses/1074.

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The Randomized Gauss-Seidel Method (RGS) is an iterative algorithm that solves overdetermined systems of linear equations Ax = b. This paper studies an update on the RGS method, the Randomized Block Gauss-Seidel Method. At each step, the algorithm greedily minimizes the objective function L(x) = kAx bk2 with respect to a subset of coordinates. This paper describes a Randomized Block Gauss-Seidel Method (RBGS) which uses a randomized control method to choose a subset at each step. This algorithm is the first block RGS method with an expected linear convergence rate which can be described by the properties of the matrix A and its column submatrices. The analysis demonstrates that RBGS improves RGS more when given appropriate column-paving of the matrix, a partition of the columns into well-conditioned blocks. The main result yields a RBGS method that is more e cient than the simple RGS method.

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Liang, Yunxu. "Improved Gauss-Seidel iterative method on power networks." [Gainesville, Fla.] : University of Florida, 2004. http://purl.fcla.edu/fcla/etd/UFE0008140.

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Hocking, Laird Robert. "A complex analysis based derivation of multigrid smoothing factors of lexicographic Gauss-Seidel." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/37012.

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This thesis aims to present a unified framework for deriving analytical formulas for multigrid smoothing factors in arbitrary dimensions, under certain simplifying assumptions. To derive these expressions we rely on complex analysis and geometric considerations, using the maximum modulus principle and Mobius transformations. We restrict our attention to pointwise and block lexicographic Gauss-Seidel smoothers on a d-dimensional uniform mesh, where the computational molecule of the associated discrete operator forms a 2d+1 point star. In the pointwise case the effect of a relaxation parameter, as well as different choices of mesh ratio, are analyzed. The results apply to any number of spatial dimensions, and are applicable to high-dimensional versions of a few common model problems with constant coefficients, including the Poisson and anisotropic diffusion equations as well as the convection-diffusion equation. We show that in most cases our formulas, exact under the simplifying assumptions of Local Fourier Analysis, form tight upper bounds for the asymptotic convergence of geometric multigrid in practice. We also show that there are asymmetric cases where lexicographic Gauss-Seidel smoothing outperforms red-black Gauss-Seidel smoothing; this occurs for certain model convection-diffusion equations with high mesh Reynolds numbers.

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Parks, Michael Lawrence. "Efficient Numeric Computation of a Phase Diagram in Biased Diffusion of Two Species." Thesis, Virginia Tech, 2000. http://hdl.handle.net/10919/32896.

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A lattice gas with equal numbers of oppositely charged particles, diffusing under the influence of a uniform electric field and an excluded volume condition undergoes an order-disorder phase transition, controlled by the particle density and the field strength. This transition may be continuous (second order) or continuous (first order). Results from previous discrete simulations are shown, and a theoretical continuum model is developed. As this is a nonequilibrium system, there is no associated free energy to determine the location of a first order transition. Instead, the model equations for this system are evolved in time numerically, and the locus of this transition is determined via the presence of a stable state with coexisting regions of order and disorder. The Crank-Nicholson, nonlinear Gauss-Seidel, and GMRES algorithms used to solve the model equations are discussed. Performance enhancements and limits on convergence are considered.<br>Master of Science

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Bokka, Naveen. "Comparison of Power Flow Algorithms for inclusion in On-line Power Systems Operation Tools." ScholarWorks@UNO, 2010. http://scholarworks.uno.edu/td/1237.

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The goal of this thesis is to develop a new, fast, adaptive load flow algorithm that "automatically alternates" numerical methods including Newton-Raphson method, Gauss-Seidel method and Gauss method for a load flow run to achieve less run time. Unlike the proposed method, the traditional load flow analysis uses only one numerical method at a time. This adaptive algorithm performs all the computation for finding the bus voltage angles and magnitudes, real and reactive powers for the given generation and load values, while keeping track of the proximity to convergence of a solution. This work focuses on finding the algorithm that uses multiple numerical techniques, rather than investigating programming techniques and programming languages. The convergence time is compared with those from using each of the numerical techniques. The proposed method is implemented on the IEEE 39-bus system with different contingencies and the solutions obtained are verified with PowerWorld Simulator, a commercial software for load flow analysis.

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Tazeroualti, Mohammed. "Modélisation de surfaces à l'aide de fonctions splines : conception d'un verre progressif." Grenoble 1, 1993. http://tel.archives-ouvertes.fr/tel-00343495.

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Ce travail se décompose en trois parties distinctes. Dans la première partie, on introduit un algorithme du type Gauss-Seidel pour la minimisation de fonctionnelles symétriques semi-définies positives. La convergence de cet algorithme est démontrée. En application, on donne deux méthodes de lissage de surfaces. Ces méthodes sont basées sur l'idée de ramener un probleme de lissage a deux dimensions a la resolution d'une suite de problèmes a une dimension faciles a résoudre. Pour cela on utilise l'opération d'inf-convolution spline. Dans la deuxième partie, on introduit une nouvelle methode pour la conception d'un verre progressif. Ce verre est représente par une surface suffisamment régulière, a laquelle on impose des conditions sur ses courbures principales dans certaines zones (zone de vision de loin et zone de vision de pres), et des conditions sur ses directions principales de courbure dans d'autres zones (zone nasale et zone temporale). La surface est écrite sous forme de produit tensoriel de b-splines de degré quatre. Pour la calculer, on est amené a minimiser un opérateur non quadratique. Cette minimisation est alors effectuée par un procédé itératif dont on a teste numériquement la convergence rapide

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Anderson, Curtis James. "Estimating the Optimal Extrapolation Parameter for Extrapolated Iterative Methods When Solving Sequences of Linear Systems." University of Akron / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=akron1383826559.

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Jurča, Ondřej. "Ustálený chod a zkratové poměry v síti 110 kV E.ON napájené z rozvodny 110 kV Otrokovice v roce 2011." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2011. http://www.nusl.cz/ntk/nusl-219016.

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Distribution network 110 kV owned by E. ON in the area Otrokovice; powered by 110 kV and two variants of involvement contained.The first option is basic involvement, without the use of the bridge. The second option includes involvement with the bridge. The aim of this study is to compare; by calculating the steady-state network operation and short circuit conditions of the network, the involvement of these two options. The thesis is divided into two parts, theoretical and practical. The theoretical part consists of a description of the steady operation of networks of high-voltage and short circuit ratio calculations. Load flow calculations are described by the Gauss-Seidel and Newton iterative method. In the case of short-circuit conditions, the effects of their characteristic values, processes and various methods of calculation are described.In the second part, this theoretical knowledge is applied to input data and dispatching programme with the appropriate calculations of network operation and short circuit conditions. The calculated values are listed in the thesis, on the basis of which an evaluation of the two possible connections is made.

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Book chapters on the topic "Gauss-Seidel"

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Nishida, Hiroshi, and Hairong Kuang. "Experiments on Asynchronous Partial Gauss-Seidel Method." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11573937_14.

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Dey, Suhrit. "Perturbation of Gauss-Seidel Iterations (PFI#2) [1]." In Perturbed Functional Iterations. Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003325925-4.

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Hladík, Milan. "Optimal Preconditioning for the Interval Parametric Gauss–Seidel Method." In Scientific Computing, Computer Arithmetic, and Validated Numerics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31769-4_10.

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Morgül, Ö., and A. Malaş. "Application of Gauss-Seidel Iteration to the RLS Algorithm." In Linear Algebra for Large Scale and Real-Time Applications. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-015-8196-7_47.

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Freundl, Christoph, and Ulrich Rüde. "Gauss-Seidel Iterative Method for the Computation of Physical Problems." In Algorithms Unplugged. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-15328-0_30.

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Strout, Michelle Mills, Larry Carter, Jeanne Ferrante, Jonathan Freeman, and Barbara Kreaseck. "Combining Performance Aspects of Irregular Gauss-Seidel Via Sparse Tiling." In Languages and Compilers for Parallel Computing. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11596110_7.

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Tay, Lea Tien, Tze Hoe Foong, and Janardan Nanda. "Some New Findings on Gauss–Seidel Technique for Load Flow Analysis." In Lecture Notes in Electrical Engineering. Springer Singapore, 2014. http://dx.doi.org/10.1007/978-981-4585-42-2_60.

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Guo, Peng, and Shi-liang Wu. "A Modified Gauss-Seidel Iteration Method for Solving Absolute Value Equations." In Simulation Tools and Techniques. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72792-5_13.

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Larsen, Martin, and Per Madsen. "A Scalable Parallel Gauss-Seidel and Jacobi Solver for Animal Genetics." In Recent Advances in Parallel Virtual Machine and Message Passing Interface. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-48158-3_44.

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Zhao, Xiaoqing, Zhengquan Li, Qiong Wu, et al. "An Improved Gauss-Seidel Algorithm for Signal Detection in Massive MIMO Systems." In Wireless and Satellite Systems. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-19156-6_37.

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Conference papers on the topic "Gauss-Seidel"

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Sanitha Michail, C., M. R. Rashmi, and Vigna K. Ramachandaramurthy. "Power Flow Analysis in Microgrid Using Gauss-Seidel Method." In 2024 First International Conference on Innovations in Communications, Electrical and Computer Engineering (ICICEC). IEEE, 2024. https://doi.org/10.1109/icicec62498.2024.10808319.

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Tseng, Chien-Cheng, and Su-Ling Lee. "Noise Reduction of Temperature Data Using Jacobi and Gauss-Seidel Iterations." In 2024 International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS). IEEE, 2024. https://doi.org/10.1109/ispacs62486.2024.10868871.

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Park, Han Jin, Heesang Chung, Sung-Woo Choi, and Jeong Woo Lee. "Coded Multi-User Extreme Massive MIMO Systems with Gauss Seidel-Aided MMSE-PIC." In 2024 15th International Conference on Information and Communication Technology Convergence (ICTC). IEEE, 2024. https://doi.org/10.1109/ictc62082.2024.10826779.

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Ismail, Nurulhuda, Khairun Nidzam Ramli, Ariffuddin Joret, Mohamad Hairol Jabbar, Norshidah Katiran, and Eddy Irwan Shah Saadon. "A Joint Gauss-Seidel and Neumann Series Precoding Scheme for a Downlink Massive MIMO System." In 2025 21st IEEE International Colloquium on Signal Processing & Its Applications (CSPA). IEEE, 2025. https://doi.org/10.1109/cspa64953.2025.10933082.

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Wallin, Dan, Henrik Löf, Erik Hagersten, and Sverker Holmgren. "Multigrid and Gauss-Seidel smoothers revisited." In the 20th annual international conference. ACM Press, 2006. http://dx.doi.org/10.1145/1183401.1183423.

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Hhonghao, He, Yuan Dongjin, Hou Yi, and Xu Jinqiu. "Preconditioned Gauss-Seidel Iterative Method for Linear Systems." In 2009 International Forum on Information Technology and Applications (IFITA). IEEE, 2009. http://dx.doi.org/10.1109/ifita.2009.339.

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Hu, Changjun, Jilin Zhang, Jue Wang, and Jianjiang Li. "Parallel iteration space alternate tiling Gauss-Seidel solver." In 2007 IEEE International Conference on Cluster Computing (CLUSTER). IEEE, 2007. http://dx.doi.org/10.1109/clustr.2007.4629262.

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Day, Khaled, and Mohammad H. Al-Towaiq. "Parallel Gauss-Seidel on a Torus NoC Architecture." In Artificial Intelligence and Applications. ACTAPRESS, 2013. http://dx.doi.org/10.2316/p.2013.795-025.

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Wang, Qi, Han Hai, Kaizhi Peng, Binbin Xu, and Xue-Qin Jiang. "A Learnable Gauss-Seidel Detector for MIMO Detection." In 2020 IEEE/CIC International Conference on Communications in China (ICCC). IEEE, 2020. http://dx.doi.org/10.1109/iccc49849.2020.9238938.

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Cetinaslan, Ozan, and Rafael Oliveira Chaves. "Energy Embedded Gauss-Seidel Iteration for Soft Body Simulations." In 2019 32nd SIBGRAPI Conference on Graphics, Patterns and Images (SIBGRAPI). IEEE, 2019. http://dx.doi.org/10.1109/sibgrapi.2019.00028.

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Reports on the topic "Gauss-Seidel"

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Juang, F., and C. W. Gear. Accuracy increase in waveform Gauss Seidel. Office of Scientific and Technical Information (OSTI), 1989. http://dx.doi.org/10.2172/5977080.

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Kushner, Harold J. The Gauss-Seidel Numerical Procedure for Markov Stochastic Games. Defense Technical Information Center, 2003. http://dx.doi.org/10.21236/ada459436.

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Kushner, Harold J. The Gauss-Seidel Numerical Procedure for Markov Stochastic Games. Defense Technical Information Center, 2004. http://dx.doi.org/10.21236/ada460599.

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