Log in

Relevant bibliographies by topics / Gauss-Seidel / Journal articles

To see the other types of publications on this topic, follow the link: Gauss-Seidel.

Journal articles on the topic 'Gauss-Seidel'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 June 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Gauss-Seidel.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

2

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

3

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

4

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

5

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.

Full text

Abstract:

<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>

APA, Harvard, Vancouver, ISO, and other styles

6

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

7

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

8

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

10

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

11

Wang, Yang, Jie Liu, Xiaoxiong Zhu, Qingyang Zhang, Shengguo Li, and Qinglin Wang. "Improving Structured Grid-Based Sparse Matrix-Vector Multiplication and Gauss–Seidel Iteration on GPDSP." Applied Sciences 13, no. 15 (2023): 8952. http://dx.doi.org/10.3390/app13158952.

Full text

Abstract:

Structured grid-based sparse matrix-vector multiplication and Gauss–Seidel iterations are very important kernel functions in scientific and engineering computations, both of which are memory intensive and bandwidth-limited. GPDSP is a general purpose digital signal processor, which is a very significant embedded processor that has been introduced into high-performance computing. In this paper, we designed various optimization methods, which included a blocking method to improve data locality and increase memory access efficiency, a multicolor reordering method to develop Gauss–Seidel fine-grained parallelism, a data partitioning method designed for GPDSP memory structures, and a double buffering method to overlap computation and access memory on structured grid-based SpMV and Gauss–Seidel iterations for GPDSP. At last, we combined the above optimization methods to design a multicore vectorization algorithm. We tested the matrices generated with structured grids of different sizes on the GPDSP platform and obtained speedups of up to 41× and 47× compared to the unoptimized SpMV and Gauss–Seidel iterations, with maximum bandwidth efficiencies of 72% and 81%, respectively. The experiment results show that our algorithms could fully utilize the external memory bandwidth. We also implemented the commonly used mixed precision algorithm on the GPDSP and obtained speedups of 1.60× and 1.45× for the SpMV and Gauss–Seidel iterations, respectively.

APA, Harvard, Vancouver, ISO, and other styles

12

S., Sathya, and Ramesh T. "Comparison of Gauss Jacobi Method and Gauss Seidel Method using Scilab." International Journal of Trend in Scientific Research and Development 3, no. 6 (2019): 1051–53. https://doi.org/10.5281/zenodo.3589302.

Full text

Abstract:

Numerical Method is the important aspects in solving real world problems that are related to Mathematics, science, medicine, business etc. In this paper, We comparing the two methods by using the scilab 6.0.2 software coding to solve the iteration problem. which are Gauss Jacobi and Gauss Seidel methods of linear equations. S. Sathya | T. Ramesh "Comparison of Gauss Jacobi Method and Gauss Seidel Method using Scilab" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29316.pdf

APA, Harvard, Vancouver, ISO, and other styles

13

Sukarna, S., Muhammad Abdy, and R. Rahmat. "Perbandingan Metode Iterasi Jacobi dan Metode Iterasi Gauss-Seidel dalam Menyelesaikan Sistem Persamaan Linear Fuzzy." Journal of Mathematics, Computations, and Statistics 2, no. 1 (2020): 1. http://dx.doi.org/10.35580/jmathcos.v2i1.12447.

Full text

Abstract:

Penelitian ini mengkaji tentang menyelesaian Sistem Persamaan Linear Fuzzy dengan Membanding kan Metode Iterasi Jacobi dan Metode Iterasi Gauss-Seidel. Metode iterasi Jacobi merupakan salah satu metode tak langsung, yang bermula dari suatu hampiran Metode iterasi Jacobi ini digunakan untuk menyelesaikan persamaan linier yang proporsi koefisien nol nya besar. Iterasi dapat diartikan sebagai suatu proses atau metode yang digunakan secara berulang-ulang (pengulangan) dalam menyelesaikan suatu permasalahan matematika ditulis dalam bentuk . Pada metode iterasi Gauss-Seidel, nilai-nilai yang paling akhir dihitung digunakan di dalam semua perhitungan. Jelasnya, di dalam iterasi Jacobi, menghitung dalam bentuk . Setelah mendapatkan Hasil iterasi kedua Metode tersebut maka langkah selanjutnya membandingkan kedua metode tersebut dengan melihat jumlah iterasinya dan nilai Galatnya manakah yang lebih baik dalam menyelesaikan Sistem Persamaan Linear Fuzzy.Kata kunci: Sistem Persamaan Linear Fuzzy, Metode Itersi Jacobi, Metode Iterasi Gauss-Seidel. This study examines the completion of the Linear Fuzzy Equation System by Comparing the Jacobi Iteration Method and the Gauss-Seidel Iteration Method. The Jacobi iteration method is one of the indirect methods, which stems from an almost a method of this Jacobi iteration method used to solve linear equations whose proportion of large zero coefficients. Iteration can be interpreted as a process or method used repeatedly (repetition) in solving a mathematical problem written in the form . In the Gauss-Seidel iteration method, the most recently calculated values are used in all calculations. Obviously, inside Jacobi iteration, counting in form After obtaining the result of second iteration of the Method then the next step compare both methods by seeing the number of iteration and the Error value which is better in solving Linear Fuzzy Equation System.Keywords: Linear Fuzzy Equation System, Jacobi Itersi Method, Gauss-Seidel Iteration Method.

APA, Harvard, Vancouver, ISO, and other styles

14

Greenberg, Albert G., and Robert J. Vanderbei. "Quicker Convergence for Iterative Numerical Solutions to Stochastic Problems: Probabilistic Interpretations, Ordering Heuristics, and Parallel Processing." Probability in the Engineering and Informational Sciences 4, no. 4 (1990): 493–521. http://dx.doi.org/10.1017/s0269964800001790.

Full text

Abstract:

Gauss-Seidel is a general method for solving a system of equations (possibly nonlinear). It makes repeated sweeps through the variables; within a sweep as each new estimate for a variable is computed, the current estimate for that variable is replaced with the new estimate immediately, instead of on completion of the sweep. The idea is to use new data as soon as it is computed. Gauss- Seidel is often efficient for computing the invariant measure of a Markov chain (especially if the transition matrix is sparse), and for computing the value function in optimal control problems. In many applications the computation can be significantly improved by appropriately ordering the variables within each sweep. A simple heuristic is presented here for computing an ordering that quickens convergence. In parallel processing, several variables must be computed simultaneously, which appears to work against Gauss-Seidel. Simple asynchronous parallel Gauss-Seidel methods are presented here. Experiments indicate that the methods retain the benefit of a good ordering, while further speeding up convergence by a factor of P if P processors participate.In this paper, we focus on the optimal stopping problem. A probabilistic interpretation of the Gauss-Seidel (and the Jacobi) method for computing the value function is given, which motivates our ordering heuristic. However, the ordering heuristic and parallel processing methods apply in a broader context, in particular, to the important problem of computing the invariant measure of a Markov chain.

APA, Harvard, Vancouver, ISO, and other styles

15

Koneru, S. R., and V. B. Kumar Vatti. "Extrapolated accelerated gauss-seidel methods." International Journal of Computer Mathematics 21, no. 3-4 (1987): 311–18. http://dx.doi.org/10.1080/00207168708803573.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Ihsan, Hisyam, Maya Sari Wahyuni, and Yully Sofyah Waode. "Penerapan Metode Iterasi Jacobi dan Gauss-Seidel dalam Menyelesaikan Sistem Persamaan Linear Kompleks." Journal of Mathematics, Computations and Statistics 7, no. 1 (2024): 34–54. http://dx.doi.org/10.35580/jmathcos.v7i1.1964.

Full text

Abstract:

Penelitian ini adalah penelitian murni yang bertujuan untuk mengetahui penerapan metode iterasi jacobi dan gauss-seidel dalam menyelesaikan sistem persamaan linear kompleks baik secara manual maupun dengan menggunakan program aplikasi Matlab. Sistem persamaan linear yang digunakan adalah sistem yang memiliki 4 persamaan dengan 4 variabel, 5 persamaan dengan 5 variabel dan 6 persamaan dengan 6 variabel. Galat yang digunakan pada penelitian ini adalah dengan tebakan awal = 0. Setelah mendapatkan hasil iterasi menggunakan kedua metode tersebut maka selanjutnya membandingan antara kedua metode tersebut dengan melihat banyaknya iterasi. Berdasarkan penelitian ini diperoleh hasil bahwa metode iterasi jacobi dan gauss-seidel dapat diterapkan untuk menyelesaikan sistem persamaan linear kompleks serta metode gauss-seidel lebih baik digunakan untuk menyelesaikan sistem persamaan linear kompleks karena mempunyai iterasi yang lebih sedikit.

APA, Harvard, Vancouver, ISO, and other styles

17

Hatun, Metin. "Identification of Wiener Systems with Recursive Gauss-Seidel Algorithm." Elektronika ir Elektrotechnika 29, no. 5 (2023): 4–10. http://dx.doi.org/10.5755/j02.eie.35119.

Full text

Abstract:

The Recursive Gauss-Seidel (RGS) algorithm is presented that is implemented in a one-step Gauss-Seidel iteration for the identification of Wiener output error systems. The RGS algorithm has lower processing intensity than the popular Recursive Least Squares (RLS) algorithm due to its implementation using one-step Gauss-Seidel iteration in a sampling interval. The noise-free output samples in the data vector used for implementation of the RGS algorithm are estimated using an auxiliary model. Also, a stochastic convergence analysis is presented, and it is shown that the presented auxiliary model-based RGS algorithm gives unbiased parameter estimates even if the measurement noise is coloured. Finally, the effectiveness of the RGS algorithm is verified and compared with the equivalent RLS algorithm by computer simulations.

APA, Harvard, Vancouver, ISO, and other styles

18

Daniel, E. E., D. O. Oyewole, S. A. Akinwunmi, and D. B. Awudang. "COMPARATIVE ANALYSIS OF GAUSS SEIDEL, CONJUGATE GRADIENT AND SUCCESSIVEOVER RELAXATION FOR THE SOLUTION OF NONSYMETRIC LINEAR EQUATIONS." FULafia Journal of Science and Technology 9, no. 1 (2025): 1–6. https://doi.org/10.62050/fjst2025.v9n1.349.

Full text

Abstract:

This study undertakes a comparative analysis of three widely used computational methods namely; Gauss-Seidel, Conjugate Gradient, and Successive Over-Relaxation (SOR) for solving nonsymmetric linear equations. The main goal is to assess the effectiveness, efficiency and convergence rates of these methods when applied to nonsymmetric linear systems, which frequently occurs in scientific and engineering problems. The Gauss-Seidel method, knownfor its iterative simplicity and straightforward implementation, is compared with the Conjugate Gradient method, which is acclaimed for its robustness and efficiency in handling large and sparse systems. The SOR method, an optimized version of Gauss-Seidel, was also evaluated to determine its potentials for accelerating convergence. Through a series of numerical experiments and performance benchmarks, the study reveals that the ConjugateGradient method consistently outperforms the other two methods in terms of convergence, speed and computational efficiency, particularly for large-scale nonsymmetric systems. The Gauss-Seidel and SOR methods, while showing competitive performance for smaller or less complex systems, do not match the efficiency of the Conjugate Gradient method in more demanding scenarios. Based on the results, the Conjugate Gradient method is recommended as the preferred choice for solving large nonsymmetric linear systems due to its superior performance.

APA, Harvard, Vancouver, ISO, and other styles

19

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.

Full text

Abstract:

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 Hâmatrices (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 Hâmatrices. 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 Hâmatrices. Then, the convergence results on preconditioned Gauss-Seidel (PGS) iterative methods for general Hâmatrices are presented. Finally, some numerical examples are given to demonstrate the results obtained in this paper.

APA, Harvard, Vancouver, ISO, and other styles

20

Kim, Y. J., and S. B. Lee. "A ROBUST CODE OF GAUSS-SEIDEL SMOOTHER IN OPENFOAM." Journal of Computational Fluids Engineering 24, no. 2 (2019): 43–49. http://dx.doi.org/10.6112/kscfe.2019.24.2.043.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Zhou, Bo Jian, Xu Hong Li, and Jie He. "A Comparative Study of Two Alternative Methods for the Path-Based Logit Stochastic User Equilibrium Problem." Advanced Materials Research 756-759 (September 2013): 1433–36. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.1433.

Full text

Abstract:

in this paper, a computational study of two alternative methods for the path-based logit stochastic user equilibrium model is conducted. The two methods under investigation are the Jacobi gradient projection method and the Gauss-Seidel gradient projection method. We compare the two methods on the Sioux Falls network. Numerical results indicate that for the path-based logit SUE problem, Jacobi gradient projection method is more efficient than Gauss-Seidel gradient projection method.

APA, Harvard, Vancouver, ISO, and other styles

22

Nurullaeli, Nurullaeli. "Media Analisis Rangkaian Listrik Menggunakan Pendekatan Numerik Gauss-Jordan, Gauss-Seidel, dan Cramer." Navigation Physics : Journal of Physics Education 2, no. 1 (2020): 1–8. http://dx.doi.org/10.30998/npjpe.v2i1.245.

Full text

Abstract:

The aim of this study is create an analysis media for calculating the electric current in a closed circuit with one or more loops. Gauss-Jordan, Gauss-Seidel, and Cramer methods were used in this study. This media is packaged into Graphic User Interface (GUI) with matlab language program assisting. In this study, Linear Equation System (SPL) was obtained from kirchhoff current law and kirchhoff voltage law concepts. Gauss-Seidel method is not always convergent for each formed SPL, because it can only be applied when coefficient matrix A was diagonally dominant. The application of this analysis media made the calculation of closed circuit electric current with one or more loops became accurate and time saving.

APA, Harvard, Vancouver, ISO, and other styles

23

Pikutić, Marko, Goran Grdenić, and Marko Delimar. "Comparison of results and calculation speeds of various power system power flow methods." Journal of Energy - Energija 66, no. 1-4 (2022): 117–27. http://dx.doi.org/10.37798/2017661-4100.

Full text

Abstract:

The theoretical part describes basic power flow methods Gauss-Seidel and Newton-Raphson in their practical forms for solving a load flow problem. In practical part, IEEE test 24, 48 and 72 node networks are used to compare basic methods in terms of calculation speed: on execution of one iteration, entire calculation and on given accuracy influence. Also is analyzed optimal acceleration factor for Gauss-Seidel method and convergences of methods. On the end, final conclusions are obtained after analyzing comparison results.

APA, Harvard, Vancouver, ISO, and other styles

24

Mohamed Amine, Benhari, and Kaicer Mohammed. "Analysis of uncertainty in the Leontief model by interval arithmetic." Statistics, Optimization & Information Computing 13, no. 5 (2025): 2011–26. https://doi.org/10.19139/soic-2310-5070-2279.

Full text

Abstract:

This paper presents an innovative strategy to enhance the precision of economic projections through the integration of interval arithmetic into the Leontief model. We emphasise the utilisation of the Gauss-Seidel method for solving linear systems with interval coefficients. In this paper, we present a method that use the Gauss-Seidel approach to effectively solve linear systems consisting of interval coefficients. This technique enhances traditional methods by incorporating potential value intervals, in addition to exact numerical values. The result is a more precise reflection of uncertainty and a more accurate calculation of solution intervals for economic variables. We have implemented this approach in the Moroccan economic context and the Washington state context using the Gauss-Seidel method to solve linear systems with interval coefficients. Based on real economic data, we have demonstrated how this technique can have a positive impact on the accuracy of output and sensitivity evaluations in the Leontief model.

APA, Harvard, Vancouver, ISO, and other styles

25

Milaszewicz, J. P. "Improving Jacobi and Gauss-Seidel Iterations." Linear Algebra and its Applications 93 (August 1987): 161–70. http://dx.doi.org/10.1016/s0024-3795(87)90321-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Křížek, Michal, Liping Liu, and Pekka Neittaanmäki. "Post‐processing of Gauss–Seidel iterations." Numerical Linear Algebra with Applications 6, no. 2 (1999): 147–56. http://dx.doi.org/10.1002/(sici)1099-1506(199903)6:2<147::aid-nla153>3.0.co;2-u.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Akram, Muhammad, Ghulam Muhammad, Ali N. A. Koam, and Nawab Hussain. "Iterative Methods for Solving a System of Linear Equations in a Bipolar Fuzzy Environment." Mathematics 7, no. 8 (2019): 728. http://dx.doi.org/10.3390/math7080728.

Full text

Abstract:

We develop the solution procedures to solve the bipolar fuzzy linear system of equations (BFLSEs) with some iterative methods namely Richardson method, extrapolated Richardson (ER) method, Jacobi method, Jacobi over-relaxation (JOR) method, Gauss–Seidel (GS) method, extrapolated Gauss-Seidel (EGS) method and successive over-relaxation (SOR) method. Moreover, we discuss the properties of convergence of these iterative methods. By showing the validity of these methods, an example having exact solution is described. The numerical computation shows that the SOR method with ω = 1 . 25 is more accurate as compared to the other iterative methods.

APA, Harvard, Vancouver, ISO, and other styles

28

Sa'adah, Maria Syifaus, and Evawati Alisah. "Interpretasi Metode Gauss-Seidel pada Sistem Persamaan Linier Fuzzy dengan Bilangan Fuzzy Sigmoid." Jurnal Riset Mahasiswa Matematika 3, no. 5 (2024): 223–40. http://dx.doi.org/10.18860/jrmm.v3i5.27320.

Full text

Abstract:

A system of linear equations can be combined with a fuzzy number that produces a new equation, namely a system of fuzzy linear equations. The system of fuzzy linear equations has the general form , as an element with real numbers, as a variable of fuzzy numbers, and as a constant of fuzzy numbers. One kind of fuzzy number is sigmoid fuzzy number. The problem related to the system of fuzzy linear equations is how to solve the system of fuzzy linear equations. One method that can be used is using the Gauss-Seidel Method. This study aims to determine the results of the interpretation of the Gauss-Seidel Method to determine the solution of the fuzzy linear equation system. Based on the calculation results, it shows that the Gauss-Seidel Method does not always provide the right solution for fuzzy linear equation systems with fuzzy variables and constants in the form of sigmoid numbers expressed as cuts. The solution is considered correct if the substitution of the solution to the system of fuzzy linear equations and defuzzification and shows the same result.

APA, Harvard, Vancouver, ISO, and other styles

29

Dulhadi, Dulhadi, Mohammad Arsyad, Shodiq Afifudin, Eufrasia Andranetta Gracelynne Eka Pramudita, Hafiyyan Putra Pratama, and Dewi Indriati Hadi Putri6. "METODE NUMERIK UNTUK ANALISIS KUALITAS SISTEM KELISTRIKAN BANDARA YOGYAKARTA INTERNATIONAL AIRPORT." KURVATEK 8, no. 2 (2023): 121–32. http://dx.doi.org/10.33579/krvtk.v8i2.4585.

Full text

Abstract:

Kualitas distribusi energi listrik secara praktis ditentukan dari drop tegangan dan faktor daya. Batasan drop tegangan terstandar 10% < tegangan kerja nominal < 5% dan faktor daya terendah 0,85. Untuk menganalisa kualitas sistem kelistrikan Bandara Yogyakarta International Airport (YIA) diperlukan perhitungan aliran daya yang tepat diantaranya penerapan metode Newton Raphson, Fast Decouple dan Gauss – Seidel. Tingkat kerumitan penyelesaian aliran daya sistem kelistrikan Bandara YIA secara manual cukup tinggi. Oleh karenya program aplikasi Etap versi 12.6 dapat menyelesaikan permasalah tersebut. Dengan membandingkan ketiga metode tersebut, pada iterasi 99, indeks presisi 10-4 metode Newton Raphson dan Fast Decouple memiliki kesederhaaan implementasi, effisiensi perhitungan dan keandalan yang tinggi dibandingkan Gauss – Seidel. Hasil running Newton Raphson dan Fast Decouple memiliki kesamaan hasil yaitu faktor daya dibawah standar 5 titik beban dari 41 titik beban (12,19%) dan drop tegangan tertinggi 2,48 %, Gauss-Seidel dengan iterasi 2000, nilai indeks prsisi 10-6 menghasilkan 7 titik beban (17,07%). Dengan demikian metode Newton Raphson atau Fast Decouple dapat digunakan untuk analisa kualitas sistem kelistrikan Bandara YIA. Kesimpulan hasil running menyimpulkan bahwa kondisi kualitas sistem kelistrikan Bandara YIA masih diatas standar.

APA, Harvard, Vancouver, ISO, and other styles

30

Dessalew, Gashaye, Tesfaye Kebede, Gurju Awgichew, and Assaye Walelign. "Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices." Abstract and Applied Analysis 2021 (May 31, 2021): 1–7. http://dx.doi.org/10.1155/2021/8343207.

Full text

Abstract:

This paper presents generalized refinement of Gauss-Seidel method of solving system of linear equations by considering consistently ordered 2-cyclic matrices. Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. To observe the effectiveness of this method, few numerical examples are given. The study points out that, using the generalized refinement of Gauss-Seidel method, we obtain a solution of a problem with a minimum number of iteration and obtain a greater rate of convergence than other previous methods.

APA, Harvard, Vancouver, ISO, and other styles

31

Krause, Rolf, and Martin Weiser. "Multilevel augmented Lagrangian solvers for overconstrained contact formulations." ESAIM: Proceedings and Surveys 71 (August 2021): 175–84. http://dx.doi.org/10.1051/proc/202171175.

Full text

Abstract:

Multigrid methods for two-body contact problems are mostly based on special mortar discretizations, nonlinear Gauss-Seidel solvers, and solution-adapted coarse grid spaces. Their high computational efficiency comes at the cost of a complex implementation and a nonsymmetric master-slave discretization of the nonpenetration condition. Here we investigate an alternative symmetric and overconstrained segment-to-segment contact formulation that allows for a simple implementation based on standard multigrid and a symmetric treatment of contact boundaries, but leads to nonunique multipliers. For the solution of the arising quadratic programs, we propose augmented Lagrangian multigrid with overlapping block Gauss-Seidel smoothers. Approximation and convergence properties are studied numerically at standard test problems.

APA, Harvard, Vancouver, ISO, and other styles

32

Ahmadi, Afshin, Felice Manganiello, Amin Khademi, and Melissa C. Smith. "A Parallel Jacobi-Embedded Gauss-Seidel Method." IEEE Transactions on Parallel and Distributed Systems 32, no. 6 (2021): 1452–64. http://dx.doi.org/10.1109/tpds.2021.3052091.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Wen, R. P. "Self-adaptive Extrapolated Gauss-Seidel Iterative Methods." Journal of Mathematical Study 48, no. 1 (2015): 18–29. http://dx.doi.org/10.4208/jms.v48n1.15.02.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Meng, Qingwen, Xuyou Li, and Yanda Guo. "An Efficient Gauss-Seidel Cubature Kalman Filter." IEEE Transactions on Circuits and Systems II: Express Briefs 69, no. 3 (2022): 1932–36. http://dx.doi.org/10.1109/tcsii.2021.3121007.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Hatun, Metin. "Tekrarlamalı Gauss-Seidel Algoritması ile İşaret Modelleme." Academic Perspective Procedia 3, no. 1 (2020): 626–34. http://dx.doi.org/10.33793/acperpro.03.01.116.

Full text

Abstract:

Periyodik işaretler Fourier serisi a&amp;ccedil;ılımı kullanılarak harmonik bileşenlerinin toplamı cinsinden ifade edilebilmektedir. Periyodik işaretlerin harmonik bileşenlerinin katsayılarını tahmin etmek i&amp;ccedil;in son yıllarda literat&amp;uuml;rde &amp;ccedil;eşitli sistem tanıma algoritmaları kullanılmıştır. Bu &amp;ccedil;alışmada periyodik işaretlerin harmonik bileşenlerinin parametrelerini ger&amp;ccedil;ek zamanda tahmin edebilmek i&amp;ccedil;in, bir adım Gauss-Seidel iterasyonu kullanılarak elde edilen RGS (Recursive Gauss-Seidel) algoritması &amp;ouml;nerilmiştir. Tekrarlamalı bir algoritma olan RGS algoritması &amp;ccedil;evrim-i&amp;ccedil;i parametre tahmini i&amp;ccedil;in uygun bir algoritmadır. Yapılan bilgisayar benzetimleriyle, &amp;ouml;nerilen RGS algoritması harmonik parametrelerinin tahmin edilmesinde kullanılmış ve benzer sistem tanıma algoritmalarıyla karşılaştırmalı olarak incelenmiştir.

APA, Harvard, Vancouver, ISO, and other styles

36

Bela Amelia. "Sistem Persamaan Linear dengan Metode Gauss Seidel." Jurnal Pustaka Cendekia Pendidikan 2, no. 2 (2024): 132–36. https://doi.org/10.70292/jpcp.v2i2.22.

Full text

Abstract:

A linear equation is an algebraic equation in which each term contains a constant or multiplication of a constant with a single variable. Systems of linear equations arise directly from real problems that require a solution process. Systems of linear equations can be solved by two methods. The first method is direct, which is usually called the exact method. These methods include inverse, elimination, substitution, LU decomposition, Cholesky decomposition, QR decomposition, Crout decomposition, and ST decomposition. The second method is usually known as the indirect method or iteration method, including the Jacobi iteration method, the Newton method, and the Gauss Seidel method. The Gauss-Seidel method is a method of solving simultaneous equations through an iteration process so that the actual value is obtained by using the initial value in the next process using a previously known value.

APA, Harvard, Vancouver, ISO, and other styles

37

Usui, Masataka, Hiroshi Niki, and Toshiyuki Kohno. "Adaptive gauss-seidel method for linear systems." International Journal of Computer Mathematics 51, no. 1-2 (1994): 119–25. http://dx.doi.org/10.1080/00207169408804271.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Adams, Mark, Marian Brezina, Jonathan Hu, and Ray Tuminaro. "Parallel multigrid smoothing: polynomial versus Gauss–Seidel." Journal of Computational Physics 188, no. 2 (2003): 593–610. http://dx.doi.org/10.1016/s0021-9991(03)00194-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Zou, Youyi Jiang Limin. "Convergence of The Gauss-Seidel Iterative Method." Procedia Engineering 15 (2011): 1647–50. http://dx.doi.org/10.1016/j.proeng.2011.08.307.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

黄, 江玲. "Convergence of Preconditioned Gauss-Seidel Iterative Method." Pure Mathematics 10, no. 11 (2020): 1007–13. http://dx.doi.org/10.12677/pm.2020.1011119.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Zhongzhi, Bai, and Wang Deren. "Asynchronous multisplitting nonlinear Gauss-Seidel type method." Applied Mathematics 9, no. 2 (1994): 189–94. http://dx.doi.org/10.1007/bf02662072.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Kearfott, R. Baker. "Preconditioners for the Interval Gauss–Seidel Method." SIAM Journal on Numerical Analysis 27, no. 3 (1990): 804–22. http://dx.doi.org/10.1137/0727047.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Zhongzhi, Bai, and Wang Deren. "Asynchronous parallel multisplitting nonlinear gauss-seidel iteration." Applied Mathematics-A Journal of Chinese Universities 12, no. 2 (1997): 179–94. http://dx.doi.org/10.1007/s11766-997-0019-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Xu, Ning, and Zhonghua Jiang. "Thermal aware floorplanning using Gauss-Seidel method." Journal of Electronics (China) 25, no. 6 (2008): 845–51. http://dx.doi.org/10.1007/s11767-008-0025-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Li, W., P. M. Pardalos, and C. G. Han. "Gauss-seidel method for least-distance problems." Journal of Optimization Theory and Applications 75, no. 3 (1992): 487–500. http://dx.doi.org/10.1007/bf00940488.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Park, Sangjoon. "Gauss-Seidel Approximation Based Static OSIC Scheme for MIMO Systems." Journal of Korean Institute of Communications and Information Sciences 47, no. 9 (2022): 1298–301. http://dx.doi.org/10.7840/kics.2022.47.9.1298.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Cheng, Peng, Jumat Sulaiman, Khadizah Ghazali, Majid Khan Majahar Ali, and Ming Ming Xu. "New Newton Group Iterative Methods for Solving Large-Scale Multi-Objective Constrained Optimization Problems." European Journal of Pure and Applied Mathematics 18, no. 1 (2025): 5551. https://doi.org/10.29020/nybg.ejpam.v18i1.5551.

Full text

Abstract:

With the rapid development of big data and artificial intelligence technologies, we are facing increasingly complex data and decision-making problems. Solving large-scale multi-objective constrained optimization problems can help to solve many practical engineering and scientific problems. The weighted and Lagrange multiplier methods are considered to be classical and effective methods for dealing with multiple objectives and constraints, but there are some difficulties in solving the processed unconstrained optimization problems.The Newton method is a commonly used method for solving this type of problem, but it requires a high computational complexity. In order to solve these difficulties, we combine four methods such as the Weighted method, Lagrange multiplier method, Newton's method and Explicit Group Gauss-Seidel iterative method to propose new Newton Group iterative methods such as 2 and 4-point Explicit Group Gauss-Seidel iterative methods namely as Newton-2EGGS and Newton-4EGGS for solving large-scale multi-objective constrained optimization problems. Also, the convergence analysis of the proposed method is presented. To test the superiority of the proposed method by comparing the computational results, the Newton-4EGGS iteration is more efficient than both Newton-2EGGS iterative method and the Newton-Gauss-Seidel iterative method (Newton-GS), especially in terms of the number of iterations and the computational time.

APA, Harvard, Vancouver, ISO, and other styles

48

Hussain, Md Delwar, Md Hamidur Rahman, and Nur Mohammad Ali. "Investigation of Gauss-Seidel Method for Load Flow Analysis in Smart Grids." Scholars Journal of Engineering and Technology 12, no. 05 (2024): 169–78. http://dx.doi.org/10.36347/sjet.2024.v12i05.004.

Full text

Abstract:

Load flow analysis is essential for understanding and optimizing power system operations. It helps in determining the steady-state behavior of power systems, ensuring efficient and reliable energy transmission. This study aims to analyze a 5-bus power system using the Gauss-Seidel method for load flow analysis. The objective is to calculate steady-state voltages, voltage angles, real and reactive power flows, line losses, and overall reactive and active power losses. The Gauss-Seidel method is employed due to its suitability for small systems and ease of understanding. The method iteratively calculates the voltage magnitude and phase angle at each bus until convergence is achieved. The analysis reveals the steady-state conditions of the 5-bus power system. The calculated results include voltage magnitudes, voltage angles, real and reactive power flows, line losses, and overall reactive and active power losses. The analysis also provides insights into the system’s operating conditions and helps identify potential areas for improvement. The Gauss-Seidel method proves to be effective in analyzing small power systems, providing accurate results with minimal computational complexity. The study demonstrates the importance of load flow analysis in understanding power system behavior and optimizing system operations. The results highlight the significance of considering reactive power in power system analysis to ensure efficient energy transmission.

APA, Harvard, Vancouver, ISO, and other styles

49

Hendriansyah, Hendriansyah, Noertjahjani Siswandari, Kiswanto Aris, and Sam'an Muhammad. "Increasing the Efficiency of Electrical Load Calculations Using the Gauss-Seidel Method with Fuzzy Logic." Circuit: Jurnal Ilmiah Pendidikan Teknik Elektro 8, no. 2 (2024): 192. http://dx.doi.org/10.22373/crc.v8i2.24729.

Full text

Abstract:

Improving the accuracy of electric load calculations is a significant task in power system analysis, particularly when dealing with fluctuating loads. Despite its simplicity, the Gauss-Seidel method has historically had trouble handling rapidly changing loads. This paper introduces a novel hybrid approach that increases load computation accuracy and efficiency by fusing fuzzy logic with the Gauss-Seidel method. Fuzzy logic is used in this method to forecast load changes based on previous and present data, which makes load adjustments more precise and faster. The results demonstrate how much better this hybrid technique is than the conventional ones, with accuracy rising from 60% to 84% and efficiency rising by 35%. This makes it an excellent choice for contemporary power systems

APA, Harvard, Vancouver, ISO, and other styles

50

Zhou, Huanbo, Zhenyu Xu, Xijun Liu, and Xinyu Zhang. "A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions." Proceedings of the ACM on Computer Graphics and Interactive Techniques 8, no. 1 (2025): 1–17. https://doi.org/10.1145/3728291.

Full text

Abstract:

Simulating multi-object collisions in real-time environments remains a significant challenge, particularly when handling simultaneous collisions in a physically accurate manner. Traditional Gauss-Seidel solvers, widely employed in physics engines, often fail to preserve the symmetry and consistency of multi-object interactions that are often observed in physics. In this paper, we present a generalized and robust Gauss-Seidel solver to overcome the difficulties in simultaneous collisions. Using spatial and temporal collision states to classify and resolve constraints, our algorithm ensures correct collision propagation and symmetry, addressing the limitations commonly found in existing solvers. Moreover, our algorithm can mitigate jitters caused by floating-point errors, ensuring smooth and stable collision responses. Our approach demonstrates fast convergence and improved accuracy in scenarios involving complex multi-object collisions.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!