scholarly journals Convergence results for some piecewise linear solvers

2021 ◽  
Author(s):  
Manuel Radons ◽  
Siegfried M. Rump
Keyword(s):  
Linear Equation ◽  
Piecewise Linear ◽  
Equation System ◽  
Absolute Value Equation ◽  
Linear Solvers ◽  
Absolute Value ◽  
Numerical Tests ◽  
Convergence Results ◽  
Linear Equation System

AbstractLet A be a real $$n\times n$$ n × n matrix and $$z,b\in \mathbb R^n$$ z , b ∈ R n . The piecewise linear equation system $$z-A\vert z\vert = b$$ z - A | z | = b is called an absolute value equation. In this note we consider two solvers for uniquely solvable instances of the latter problem, one direct, one semi-iterative. We slightly extend the existing correctness, resp. convergence, results for the latter algorithms and provide numerical tests.

scholarly journals The Picard-HSS-SOR iteration method for absolute value equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Lin Zheng
Keyword(s):  
Iteration Method ◽  
Numerical Experiments ◽  
Absolute Value Equation ◽  
Absolute Value Equations ◽  
Absolute Value ◽  
Convergence Results ◽  
Hss Iteration ◽  
The Absolute ◽  
Hss Iteration Method

AbstractIn this paper, we present the Picard-HSS-SOR iteration method for finding the solution of the absolute value equation (AVE), which is more efficient than the Picard-HSS iteration method for AVE. The convergence results of the Picard-HSS-SOR iteration method are proved under certain assumptions imposed on the involved parameter. Numerical experiments demonstrate that the Picard-HSS-SOR iteration method for solving absolute value equations is feasible and effective.

Teaching Materials of Problem-Based Linear Equation System with Two-Variables for Eighth-Grade Students in Junior High School

2021 ◽  
Vol 1 (1) ◽  
pp. 119-123
Author(s):  
Nurhayati Abbas ◽  
Nancy Katili ◽  
Dwi Hardianty Djoyosuroto
Keyword(s):  
High School ◽  
Linear Equation ◽  
Junior High School ◽  
Junior High ◽  
Equation System ◽  
Eighth Grade ◽  
Teaching Material ◽  
Teaching Materials ◽  
Linear Equation System ◽  
Eighth Grade Students

This research is motivated by the lack of mathematics teaching materials that can make students learn on their own. The teaching material can be created by teachers as they are the ones who possess the knowledge about their students’ characteristics. Further, learning materials are a set of materials (information, tools, or texts) that can aid teachers and students to carry out the learning process. The two-variable linear equation system (SPLDV) is one of the mathematics materials taught to eighth-grade students of junior high school; it contains problems related to daily life. However, it is found that this material is still difficult to master by most students. Therefore, it is necessary to develop the SPLDV teaching materials that can help students learn and solve problems as well as be used as examples by teachers in developing other materials. This research aimed to make problem-based SPLDV teaching materials. The research method refers to the Four-D Model by Thiagarajan, Semmel, and Semmel (1974). It consisted of defining, designing, developing, and disseminating. The results showed that problem-based SPLDV teaching materials could be used in learning activities as the students and the teachers had shown their positive responses after going through expert assessments. This study also suggested that the teachers use this teaching material and adopt teaching materials for other similar materials.

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 ANALISIS PEMAHAMAN KONSEP PADA MATERI SISTEM PERSAMAAN LINEAR TIGA VARIABEL BERDASARKAN TEORI APOS

Sigma ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 141
Author(s):  
Ida Silfia ◽  
Yuniar Ika Putri Pranyata
Keyword(s):  
Linear Equation ◽  
Equation System ◽  
Apos Theory ◽  
Linear Equation System ◽  
Action Process ◽  
Low Ability

This research aims to describe the analysis of students to understand the concept of the Three Variable Linear Equation System (SPLTV) based on the APOS theory (Action, Process, Object and Schema). This research did in the three students class X of MA Miftahul Huda Kepanjen. With students high (A), medium (B) and low ability categories(C). The results of the study show that highly capable subjects have an understanding of the stages of APOS (action, processes, objects and schemes). Subjects who are capable of having did’t understanding at the stage of process. While low-ability subjects have an understanding of the stages of action. In this description get node action the students tight with to understand the concept of the materi. So, researcher proposition of the teacher for notice the process materi in this study mathematics.

Sensitivity Analysis and Optimization of Mechanical System Design

1988 ◽  
Author(s):  
W. J. Langner
Keyword(s):  
Linear Equation ◽  
Mechanical System ◽  
Numerical Integration ◽  
Equation System ◽  
Sensitivity Analyses ◽  
Design Parameters ◽  
Governing Equations ◽  
Integration Algorithm ◽  
Linear Equation System ◽  
The Matrix

Abstract The paper follows studies on simulation of three-dimensional mechanical dynamic systems with the help of sparse matrix and stiff integration numerical algorithms. For sensitivity analyses and the application of numerical optimization procedures it is substantial to calculate the effect of design parameters on the system behaviour by means of derivatives of state variables with respect to the design parameters. For static and quasi static analyses the computation of these derivatives from the governing equations leads to a linear equation system. The matrix of this set of linear equations shows to be the Jacobian matrix required in the numerical integration process solving the system of governing equations for the mechanical system. Thus the factorization of the matrix perfomed by the numerical integration algorithm can be reused solving the linear equation system for the state variable sensitivities. Some example demonstrate the simplicity of building the right hand sides of the linear equation system. Also it is demonstrated that the procedure proposed neatly fits into a modular concept for simulation model building and analysis.

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