scholarly journals A STUDY OF SOLVING SYSTEM OF LINEAR EQUATION USING DIFFERENT METHODS AND ITS REAL LIFE APPLICATIONS:

2021 ◽  
Vol 23 (07) ◽  
pp. 723-733
Author(s):  
Khushbu Kumari ◽  
◽  
R K Poonia ◽  
Keyword(s):  
Linear Equation ◽  
Linear Equations ◽  
Real Life ◽  
Triangular Matrix ◽  
Direct Methods ◽  
Arbitrary Field ◽  
Gauss Elimination ◽  
Row Reduction ◽  
Common Situation ◽  
General Method

Solving a system of linear equations (or linear systems or, also simultaneous equations) is a common situation in many scientific and technological problems. Many methods either analytical or numerical, have been developed to solve them so, in this paper, I will explain how to solve any arbitrary field using the different – different methods of the system of linear equation for this we need to define some concepts. Like a general method most used in linear algebra is the Gauss Elimination or variation of this sometimes they are referred as “direct methods “Basically it is an algorithm that transforms the system into an equivalent one but with a triangular matrix, thus allowing a simpler resolution, Other methods can be more effective in solving system of the linear equation like Gauss Elimination or Row Reduction, Gauss Jordan and Crammer’s rule, etc. So, in this paper I will explain this method by taking an example also, in this paper I will explain the Researcher’ works that how they explain different –different methods by taking different examples. And I worked on using these different methods in solving a single example, i.e. I will use these methods in an example. In this paper, I will explain the real-life application that how a System of Linear Equation is used in our daily life.

scholarly journals Comparison of Solution of 3x3 System of Linear Equation in Terms of Cost

2012 ◽  
Vol 4 ◽  
pp. 1-4
Author(s):  
P.V. Ubale
Keyword(s):  
Numerical Methods ◽  
Linear System ◽  
Linear Equation ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Computational Mathematics ◽  
Elimination Procedure ◽  
Gauss Elimination ◽  
Basic Approaches ◽  
The Cost

The solution of a linear system is one of the most frequently performed calculations in computational mathematics. Many numerical methods are involved to solve the system of linear equations. There are two basic approaches elimination approaches and iterative approaches are used for the solution. In this paper we describe the comparison of two popular elimination procedure simple Gauss Elimination and Gauss Jordan elimination method on to the solution of 3x3 system of linear equation and find out the cost required to implement this procedures.

scholarly journals Influence of Preconditioning and Blocking on Accuracy in Solving Markovian Models

2009 ◽  
Vol 19 (2) ◽  
pp. 207-217 ◽  
Author(s):  
Beata Bylina ◽  
Jarosław Bylina
Keyword(s):  
Markov Chains ◽  
Iterative Methods ◽  
Linear Equations ◽  
Direct Methods ◽  
Factorization Method ◽  
Markovian Models ◽  
The Matrix ◽  
Gauss Elimination ◽  
Systems Of Linear Equations ◽  
The Impact

Influence of Preconditioning and Blocking on Accuracy in Solving Markovian ModelsThe article considers the effectiveness of various methods used to solve systems of linear equations (which emerge while modeling computer networks and systems with Markov chains) and the practical influence of the methods applied on accuracy. The paper considers some hybrids of both direct and iterative methods. Two varieties of the Gauss elimination will be considered as an example of direct methods: the LU factorization method and the WZ factorization method. The Gauss-Seidel iterative method will be discussed. The paper also shows preconditioning (with the use of incomplete Gauss elimination) and dividing the matrix into blocks where blocks are solved applying direct methods. The motivation for such hybrids is a very high condition number (which is bad) for coefficient matrices occuring in Markov chains and, thus, slow convergence of traditional iterative methods. Also, the blocking, preconditioning and merging of both are analysed. The paper presents the impact of linked methods on both the time and accuracy of finding vector probability. The results of an experiment are given for two groups of matrices: those derived from some very abstract Markovian models, and those from a general 2D Markov chain.

scholarly journals Profil Berpikir Siswa dalam Menyelesaikan Soal Sistem Persamaan Linear

2019 ◽  
Vol 6 (1) ◽  
pp. 69-84
Author(s):  
K. Ayu Dwi Indrawati ◽  
Ahmad Muzaki ◽  
Baiq Rika Ayu Febrilia
Keyword(s):  
Qualitative Research ◽  
Linear Equation ◽  
Linear Equations ◽  
Equation System ◽  
Mathematical Ability ◽  
System Of Linear Equations ◽  
Mathematics Ability ◽  
Linear Equation System ◽  
Thinking Process ◽  
Descriptive Qualitative

This research aimed to describe the thinking process of students in solving the system of linear equations based on Polya stages. This study was a descriptive qualitative research involving six Year 10 students who are selected based on the teacher's advice and the initial mathematical ability categories, namely: (1) Students with low initial mathematics ability, (2) Students with moderate initial mathematics ability, and ( 3) students with high initial mathematics ability categories. The results indicated that students with low initial mathematical ability category were only able to solve the two-variable linear equation system problems. Students in the medium category of initial mathematics ability and students in the category of high initial mathematics ability were able to solve the problem in the form of a system of linear equations of two variables and a system of three-variable linear equations. However, students found it challenging to solve problems with complicated or unusual words or languages.

Strongly Oscillatory and Nonoscillatory Subspaces of Linear Equations

1975 ◽  
Vol 27 (1) ◽  
pp. 106-110 ◽  
Author(s):  
J. Michael Dolan ◽  
Gene A. Klaasen
Keyword(s):  
Linear Equation ◽  
Linear Space ◽  
Nontrivial Solution ◽  
Linear Equations ◽  
Order Equation ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Oscillatory Solutions ◽  
The Third ◽  
All Solutions

Consider the nth order linear equationand particularly the third order equationA nontrivial solution of (1)n is said to be oscillatory or nonoscillatory depending on whether it has infinitely many or finitely many zeros on [a, ∞). Let denote respectively the set of all solutions, oscillatory solutions, nonoscillatory solutions of (1)n. is an n-dimensional linear space. A subspace is said to be nonoscillatory or strongly oscillatory respectively if every nontrivial solution of is nonoscillatory or oscillatory. If contains both oscillatory and nonoscillatory solutions then is said to be weakly oscillatory.

scholarly journals A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2062
Author(s):  
Luis Fernando Grisales-Noreña ◽  
Oscar Danilo Montoya ◽  
Walter Julian Gil-González ◽  
Alberto-Jesus Perea-Moreno ◽  
Miguel-Angel Perea-Moreno
Keyword(s):  
Direct Current ◽  
Power Flow ◽  
Processing Time ◽  
Linear Equations ◽  
Triangular Matrix ◽  
Taylor Series Expansion ◽  
Distribution Networks ◽  
Matrix Formulation ◽  
Numerical Convergence ◽  
Solution Methods

This study analyzes the numerical convergence and processing time required by several classical and new solution methods proposed in the literature to solve the power-flow problem (PF) in direct-current (DC) networks considering radial and mesh topologies. Three classical numerical methods were studied: Gauss–Jacobi, Gauss–Seidel, and Newton–Raphson. In addition, two unconventional methods were selected. They are iterative and allow solving the DC PF in radial and mesh configurations. The first method uses a Taylor series expansion and a set of decoupling equations to linearize around the desired operating point. The second method manipulates the set of non-linear equations of the DC PF to transform it into a conventional fixed-point form. Moreover, this method is used to develop a successive approximation methodology. For the particular case of radial topology, three methods based on triangular matrix formulation, graph theory, and scanning algorithms were analyzed. The main objective of this study was to identify the methods with the best performance in terms of quality of solution (i.e., numerical convergence) and processing time to solve the DC power flow in mesh and radial distribution networks. We aimed at offering to the reader a set of PF methodologies to analyze electrical DC grids. The PF performance of the analyzed solution methods was evaluated through six test feeders; all of them were employed in prior studies for the same application. The simulation results show the adequate performance of the power-flow methods reviewed in this study, and they permit the selection of the best solution method for radial and mesh structures.

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