scholarly journals Perbandingan Metode Iterasi Jacobi dan Metode Iterasi Gauss-Seidel dalam Menyelesaikan Sistem Persamaan Linear Fuzzy

2020 ◽  
Vol 2 (1) ◽  
pp. 1
Author(s):  
S. Sukarna ◽  
Muhammad Abdy ◽  
R. Rahmat
Keyword(s):  
Iteration Method ◽  
Mathematical Problem ◽  
Linear Equations ◽  
Equation System ◽  
Indirect Methods ◽  
Jacobi Iteration

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. 

scholarly journals Second degree generalized Jacobi iteration method for solving system of linear equations

2016 ◽  
Vol 47 (2) ◽  
pp. 179-192
Author(s):  
Tesfaye Kebede Enyew
Keyword(s):  
Spectral Radius ◽  
Iteration Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Jacobi Iteration ◽  
Optimal Values ◽  
Second Degree

In this paper, a Second degree generalized Jacobi Iteration method for solving system of linear equations, $Ax=b$ and discuss about the optimal values $a_{1}$ and $b_{1}$ in terms of spectral radius about for the convergence of SDGJ method of $x^{(n+1)}=b_{1}[D_{m}^{-1}(L_{m}+U_{m})x^{(n)}+k_{1m}]-a_{1}x^{(n-1)}.$ Few numerical examples are considered to show that the effective of the Second degree Generalized Jacobi Iteration method (SDGJ) in comparison with FDJ, FDGJ, SDJ.

Research on Iterative Method in Solving Linear Equations on the Hadoop Platform

2013 ◽  
Vol 347-350 ◽  
pp. 2763-2768
Author(s):  
Yi Di Liu
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Linear Equations ◽  
Engineering Problems ◽  
Jacobi Iteration ◽  
Hadoop Platform ◽  
Iteration Methods ◽  
Division Operation

Solving linear equations is ubiquitous in many engineering problems, and iterative method is an efficient way to solve this question. In this paper, we propose a general iteration method for solving linear equations. Our general iteration method doesnt contain denominators in its iterative formula, and this relaxes the limits that traditional iteration methods require the coefficient aii to be non-zero. Moreover, as there is no division operation, this method is more efficient. We implement this method on the Hadoop platform, and compare it with the Jacobi iteration, the Guass-Seidel iteration and the SOR iteration. Experiments show that our proposed general iteration method is not only more efficient, but also has a good scalability.

scholarly journals Peningkatan Kemampuan Pemecahan Masalah Matematis Melalui Pembelajaran Berbasis Masalah Pada Siswa Kelas X SMK Ar-Rahman Medan

2020 ◽  
Vol 6 (1) ◽  
pp. 23-28
Author(s):  
Nilam Sari ◽  
Vera Dewi Kartini Ompusunggu ◽  
Muhammad Daliani
Keyword(s):  
Problem Solving ◽  
Mathematical Problem ◽  
Linear Equations ◽  
Sample Selection ◽  
Problem Based Learning ◽  
Equation System ◽  
Mathematical Problem Solving ◽  
Material System ◽  
Problem Solving Skills ◽  
Significant Difference

This study aims to determine: Is increasing the ability of mathematical problem solving students who get problem based learning better than students who get conventional learning. This research is a semi-experimental study with the study population as all students of all grade X students of SMK AR-Rahman Medan. The sample selection is done randomly and 2 classes are chosen. The instrument used is a test of problem solving skills with the material system of linear equations. Data in this study were analyzed using parametric analysis. Statistical analysis of data was performed by t test analysis. The results showed that: (1) Increased mathematical problem solving abilities of students who obtained problem-based learning were higher than students who obtained conventional learning; (2) There is a significant difference between improving students' mathematical problem solving abilities that obtain problem-based learning and students who obtain conventional learning; (3) Among the four aspects of problem solving, the highest average increase in the aspect of "making a mathematical model" of 0.635 with moderate criteria. Based on the results of this study, researchers suggest that problem-based learning in students can be used as an alternative for teachers to improve students' problem solving abilities, especially in the Linear Equation System material

scholarly journals A Preconditioned Iteration Method for Solving Sylvester Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jituan Zhou ◽  
Ruirui Wang ◽  
Qiang Niu
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Newton's Iteration ◽  
Gradient Based ◽  
Selection Of

A preconditioned gradient-based iterative method is derived by judicious selection of two auxil- iary matrices. The strategy is based on the Newton’s iteration method and can be regarded as a generalization of the splitting iterative method for system of linear equations. We analyze the convergence of the method and illustrate that the approach is able to considerably accelerate the convergence of the gradient-based iterative method.

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.

scholarly journals PERBEDAAN PENINGKATAN KEMAMPUAN PEMECAHAN MASALAH MATEMATIS DENGAN PENDEKATAN CONTEXTUAL TEACHING AND LEARNING DI KELAS X SMA NEGERI 2 PEMATANGSIANTAR

2020 ◽  
Vol 1 (2) ◽  
pp. 85-96
Author(s):  
Winmery Lasma Habeahan
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Mathematical Problem ◽  
Equation System ◽  
Mathematical Problem Solving ◽  
Control Group ◽  
Contextual Approach ◽  
Control Group Design ◽  
Contextual Teaching ◽  
The Difference

The purpose of this study was to determine the differences in the improvement of students' mathematical problem-solving abilities with the Contextual Teaching and Learning approach in the material of the two-variable linear equation system in class X SMA Negeri 2 Pematangsiantar. This study used an experimental method with the aim of being in accordance with the previous statement to determine the difference in students' mathematical problem-solving abilities with a contextual approach and an expository approach, with a randomized pretest-posttest control group design. The average increase in problem-solving abilities in the control class was 0.1688 while the increase in problem-solving abilities in the experimental class was 0.0085. By using the t-test (SPSS), with a value of Fcount = 10.907 and a significant level of 0.05, a significant probability is obtained 0.002 <0.05, it can be concluded that there is a difference in normalized gain or an increase in problem-solving ability with conventional and contextual approaches. Based on the average gain of the control and experimental classes, the increase in the control class using the conventional approach is higher than the experimental class with the contextual approach. The difference in increasing problem-solving abilities in conventional classrooms is possible due to differences in students' entry-level abilities, which can be seen in the average pretest of each class.

Hydrodynamic Torque Converters in Mechanical Transmission Systems: Methods and Analysis

1994 ◽  
Author(s):  
Anders Hedman
Keyword(s):  
Linear Equations ◽  
Equation System ◽  
Torque Converter ◽  
Transmission System ◽  
Mechanical Transmission ◽  
Transmission Systems ◽  
Linear Relationships ◽  
Non Linear ◽  
Computer Calculations ◽  
System Power

Methods for analysis of general mechanical transmission systems with a hydrodynamic torque converter (HTC) are presented. The methods are adapted for computer calculations. The properties of the HTC must be known, either explicitly as speed and torque characteristics, or implicitly as internal geometry (blade angles, etc.). Linear relationships between the torques and between the speeds of the shafts of the transmission system (except the HTC) are easily formulated. The HTC has coupled, non-linear, relationships for torques and speeds. Different ways of including these non-linear equations are presented. This can be implemented in a computer program. Solving the equation system yields the torque and speed of each shaft of the transmission system. Power losses can be handled.

scholarly journals Convergence Analysis of a Fourier-Based Solution Method of the Laplace Equation for a Model of Magnetic Recording

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
John L. Fleming
Keyword(s):  
Magnetic Recording ◽  
Solution Method ◽  
Infinite System ◽  
Formal Analysis ◽  
Mathematical Problem ◽  
Linear Equations ◽  
Head Model ◽  
Hard Drives ◽  
Recording Heads ◽  
Read Head

When engineers model the magnetostatic fields applied to recording heads of computer hard drives due to a magnetic recording medium, the solution of Laplace's equation must be found. A popular solution method is based on Fourier analysis. However, due to the geometry of the read head model, an interesting mathematical problem arises. The coefficients for the Fourier series solution of the desired magnetic potential satisfy an infinite system of linear equations. In practice, the infinite system is truncated to a finite system with little consideration for the effect this truncation has on the solution. The paper will provide a proper understanding of the underlying problem and a formal analysis of the effect of truncation.

Accelerated GPMHSS Method for Solving Complex Systems of Linear Equations

2017 ◽  
Vol 7 (1) ◽  
pp. 143-155 ◽  
Author(s):  
Jing Wang ◽  
Xue-Ping Guo ◽  
Hong-Xiu Zhong
Keyword(s):  
Complex Systems ◽  
Linear Systems ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Linear Equations ◽  
Splitting Method ◽  
Complex Symmetric Linear Systems ◽  
Systems Of Linear Equations ◽  
Complex Symmetric ◽  
Symmetric Systems

AbstractPreconditioned modified Hermitian and skew-Hermitian splitting method (PMHSS) is an unconditionally convergent iteration method for solving large sparse complex symmetric systems of linear equations, and uses one parameter α. Adding another parameter β, the generalized PMHSS method (GPMHSS) is essentially a twoparameter iteration method. In order to accelerate the GPMHSS method, using an unexpected way, we propose an accelerated GPMHSS method (AGPMHSS) for large complex symmetric linear systems. Numerical experiments show the numerical behavior of our new method.

scholarly journals IMPULSIVE AND REFLECTIVE STUDENTS’ UNDERSTANDING TO LINEAR EQUATIONS SYSTEM: AN ANALYSIS THROUGH APOS THEORY

MATHEdunesa ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 128-135
Author(s):  
Dinda Ayu Rachmawati ◽  
Tatag Yuli Eko Siswono
Keyword(s):  
Linear Equation ◽  
Cognitive Style ◽  
Junior High School ◽  
Linear Equations ◽  
Equation System ◽  
Mathematical Concept ◽  
Apos Theory ◽  
Process Stage ◽  
Linear Equation System ◽  
Action Process

Understanding is constructed or reconstructed by students actively. APOS theory (action, process, object, schema) is a theory that states that individuals construct or reconstruct a concept through four stages, namely: action, process, object, and scheme. APOS theory can be used to analyze understanding of a mathematical concept. This research is a qualitative research which aims to describe impulsive and reflective students’ understanding to linear equations system based on APOS theory. Data collection techniques were carried out by giving Matching Familiar Figure Test (MFFT) and concept understanding tests to 32 students of 8th grade in junior high school, then selected one subject with impulsive cognitive style and one subject with reflective cognitive style that can determine solutions set and solve story questions of linear equation system of two variables correctly, then the subjects were interviewed. The results show that there were differences between impulsive and reflective subjects at the stage of action in explaining the definition and giving non-examples of linear equation system of two variables, show the differences in initial scheme of two subjects. At the process stage, impulsive and reflective subjects determine solutions set of linear equation system of two variables. At the object stage, impulsive and reflective subjects determine characteristics of linear equation system of two variables. At the schema stage, impulsive and reflective subjects solve story questions of of linear equation system of two variables, show the final schematic similarity of two subjects.Keywords: understanding, APOS theory, linear equations system of two variables, impulsive cognitive style, reflective cognitive style.

Sign in / Sign up

Export Citation Format

Share Document