scholarly journals Rate of Convergence of Tikhonov Method of Regularization for Constrained Linear Equations with Operators Having Closed Ranges

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Milojica Jaćimović ◽  
Izedin Krnić ◽  
Oleg Obradović
Keyword(s):  
Linear Equation ◽  
Rate Of Convergence ◽  
Linear Equations ◽  
Tikhonov Method ◽  
Method Of Regularization

We derive the estimates of the rate of convergence of the Tikhonov method of regularization for a constrained operator linear equation. In case that the range of the corresponding operator is closed, the estimate is of the same order as the estimates for a linear equation without constraints.

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.

SOLVING LINEAR EQUATIONS IN L-FUNCTIONS

2014 ◽  
Vol 10 (03) ◽  
pp. 569-584
Author(s):  
J. KACZOROWSKI ◽  
A. PERELLI
Keyword(s):  
Functional Equation ◽  
Linear Equation ◽  
Dirichlet Series ◽  
Linear Equations

We describe the solutions of the linear equation aX + bY = cZ in the class of Dirichlet series with functional equation. Proofs are based on the properties of certain nonlinear twists of the L-functions.

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 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.

scholarly journals MENINGKATKAN HASIL BELAJAR MATEMATIKA SISWA MELALUI MODEL PEMBELAJARAN ROPES (REVIEW, OVERVIEW, PRESENTATION, EXERCISE, SUMMARY)

2020 ◽  
Vol 2 (1) ◽  
pp. 52-63
Author(s):  
Tammara Yuffa ◽  
Lenny Kurniati ◽  
Arie Wahyuni
Keyword(s):  
Action Research ◽  
Linear Equation ◽  
Teacher Performance ◽  
Linear Equations ◽  
Learning Model ◽  
Mathematical Learning ◽  
First Semester ◽  
Learning Mathematics ◽  
The Subject ◽  
Planning Implementation

The learning mathematics to students will be easier to master and understand the concept of linear equation material of one variable through the ROPES learning model. This study aims to determine that with the application of ROPES learning model on linear equation material of one variable can improve students’ learning result, students’ activities, and teachers’ performance. The subject of this study is the students of class VII B in the first semester at MTS Matholiul Ulum Banjaragung, Bangsri, Jepara in 2019/2020. Instruments were tests sheet and questionnaires. The type of this research is a classroom action research with two cycles where each cycle there are two meetings. The stages include planning, implementation, observation and reflection. The results showed an increase in student's ability to solve problems about linear equations of one variable. Based on reflection results in cycles 1 and II, it showed: 1) Students’ learning result is increased, in the cycle I the average result was 64.90 and in cycle II reached 73.18. 2) In cycle I of the first meeting was 59.67% categorized ‘enough’. The second was 6601% categorized ‘good’, and in the cycle II reached 81.15% categorized ‘very good’. 3) Increased teacher performance in the first cycle was 60% categorized medium, the second meeting reached 70% categorized high, and in cycle II reached 80% categorized very high.Kata kunci: Mathematical Learning Result, ROPES Learning Model.

scholarly journals Differences in Norwegian and Swedish student teachers’ explanations of solutions of linear equations

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Niclas Larson ◽  
Kerstin Larsson
Keyword(s):  
Linear Equation ◽  
Student Teachers ◽  
Teacher Educators ◽  
Linear Equations ◽  
Accurate Solution ◽  
Norwegian Student ◽  
Final Operation

This study draws on data from 146 Norwegian and 161 Swedish student teachers. They were given a correct but short and unannotated solution to the linear equation x + 5 = 4x – 1. The student teachers were invited to explain the solution provided for a fictive friend, who was absent when the teacher introduced this topic. An accurate solution of this equation contains two additive and one multiplicative operation. There are two main strategies for solving a linear equation, ‘swap sides swap signs’ (SSSS) and ‘do the same to both sides’ (DSBS). Of the Norwegian student teachers, 2/3 explained the additive steps in the solution by SSSS, while only 1/3 of the Swedish student teachers applied SSSS. Consequently, DSBS was more frequent among the Swedish student teachers regarding the additive steps. However, in the final, multiplicative step, 3/4 of the Norwegian student teachers chose to explain by DSBS. On the contrary, among the Swedish student teachers the proportion applying DSBS for the multiplicative step of the solution decreased, and almost as many provided a deficient explanation of the final operation. We discuss possible reasons for differences between the nations. We also suggest how teacher educators in both countries can use the results of this study to improve student teachers’ explanations of how to solve linear equations.

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