scholarly journals A doubly stochastic block Gauss–Seidel algorithm for solving linear equations

2021 ◽  
Vol 408 ◽  
pp. 126373
Author(s):  
Kui Du ◽  
Xiao-Hui Sun
Keyword(s):  
Linear Equations ◽  
Doubly Stochastic

scholarly journals The computation of stationary distributions of Markov chains through perturbations

1991 ◽  
Vol 4 (1) ◽  
pp. 29-46 ◽  
Author(s):  
Jeffery J. Hunter
Keyword(s):  
Stochastic Matrix ◽  
Linear Equations ◽  
Probability Vector ◽  
Doubly Stochastic ◽  
Rank One ◽  
Systems Of Linear Equations ◽  
Stationary Probability Vector ◽  
Irreducible Markov Chain ◽  
Algorithmic Procedure

An algorithmic procedure for the determination of the stationary distribution of a finite, m-state, irreducible Markov chain, that does not require the use of methods for solving systems of linear equations, is presented. The technique is based upon a succession of m, rank one, perturbations of the trivial doubly stochastic matrix whose known steady state vector is updated at each stage to yield the required stationary probability vector.

The influence of extrinsic motivation and work experience on employee performance (Case study in the Serang Baru Sub-district, Bekasi District)

2020 ◽  
Vol 5 (02) ◽  
pp. 167
Author(s):  
Nur’enny Nur’enny ◽  
Rahmat Hidayat
Keyword(s):  
Work Experience ◽  
Extrinsic Motivation ◽  
Employee Performance ◽  
Linear Equations ◽  
Test Reliability ◽  
Coefficient Of Determination ◽  
District Office ◽  
Normality Test ◽  
Observation Methods ◽  
Saturated Sample

This study aims to obtain information about extrinsic motivation and work experience and its effect on employee performance in the Serang Baru District Office. This study uses a saturated sample so that the population is the same as the sample of 80 employees, at the Serang Baru District Office. The method used is validation test, reliability test, then classical assumption test, which includes normality test and multicollinearity, as well as heteroscedasticity test, multiple linear analysis test, multiple linear equations, F test, coefficient of determination, and t test. The data of this research used observation methods and questionnaires distributed to 80 samples which were addressed to employees of the Serang Baru District Office. Based on the results of research and discussion, it can be concluded: 1) Extrinsic motivation does not affect employee performance because employees are willing to work more than expected regardless of extrinsic motivation or not. 2) Employee performance is strongly influenced by work experience. The more experience, they get while working, the more knowledge they will get. 3) Employee performance will be better with the support of experienced employees so as to increase the level of output produced.             Keywords: Employee Performance, Extrinsic Motivation, Work Experience

Optimization of Linear Equations using Genetic Algorithms

2011 ◽  
Vol 2 (3) ◽  
pp. 56-58
Author(s):  
Roshni .V Patel ◽  
◽  
Jignesh. S Patel
Keyword(s):  
Genetic Algorithms ◽  
Linear Equations

Logic-based Solvability of Max-plus Linear Equations

2020 ◽  
Author(s):  
CHEN Qi ◽  
LI Haitao ◽  
LI Ping ◽  
YANG Xinrong
Keyword(s):  
Linear Equations

On Some Properties of Semi-rings

2018 ◽  
pp. 35-50
Author(s):  
A. I. Belousov
Keyword(s):  
Linear Equations ◽  
Oriented Graph ◽  
Theoretical Computer Science ◽  
Alternative Methods ◽  
Main Role ◽  
Cost Matrix ◽  
Sequential Elimination ◽  
The Matrix ◽  
Systems Of Linear Equations ◽  
The Cost

The main objective of this paper is to prove a theorem according to which a method of successive elimination of unknowns in the solution of systems of linear equations in the semi-rings with iteration gives the really smallest solution of the system. The proof is based on the graph interpretation of the system and establishes a relationship between the method of sequential elimination of unknowns and the method for calculating a cost matrix of a labeled oriented graph using the method of sequential calculation of cost matrices following the paths of increasing ranks. Along with that, and in terms of preparing for the proof of the main theorem, we consider the following important properties of the closed semi-rings and semi-rings with iteration.We prove the properties of an infinite sum (a supremum of the sequence in natural ordering of an idempotent semi-ring). In particular, the proof of the continuity of the addition operation is much simpler than in the known issues, which is the basis for the well-known algorithm for solving a linear equation in a semi-ring with iteration.Next, we prove a theorem on the closeness of semi-rings with iteration with respect to solutions of the systems of linear equations. We also give a detailed proof of the theorem of the cost matrix of an oriented graph labeled above a semi-ring as an iteration of the matrix of arc labels.The concept of an automaton over a semi-ring is introduced, which, unlike the usual labeled oriented graph, has a distinguished "final" vertex with a zero out-degree.All of the foregoing provides a basis for the proof of the main theorem, in which the concept of an automaton over a semi-ring plays the main role.The article's results are scientifically and methodologically valuable. The proposed proof of the main theorem allows us to relate two alternative methods for calculating the cost matrix of a labeled oriented graph, and the proposed proofs of already known statements can be useful in presenting the elements of the theory of semi-rings that plays an important role in mathematical studies of students majoring in software technologies and theoretical computer science.

Determination of the metal toughness components in impact-bending test

2018 ◽  
Vol 84 (12) ◽  
pp. 68-72
Author(s):  
A. B. Maksimov ◽  
I. P. Shevchenko ◽  
I. S. Erokhina
Keyword(s):  
Crack Growth ◽  
Specific Energy ◽  
Crack Formation ◽  
Crack Nucleation ◽  
Scale Effects ◽  
Linear Equations ◽  
Bending Test ◽  
Cross Sectional ◽  
Two Samples ◽  
Sample Width

A method for separating the work of impact into two parts - the work of the crack nucleation and that of crack growth - which consists in testing two samples with the same stress concentrators and different cross-sectional dimensions at the notch site is developed. It is assumed that the work of crack nucleation is proportional to the width of the sample face on which the crack originates and the specific energy of crack formation, whereas the work of the crack growth is proportional to the length of crack development and the specific crack growth energy. In case of the sample fracture upon testing, the crack growth length is assumed equal to the sample width. Data on the work of fracture of two samples and their geometrical dimensions at the site of the notch are used to form a system of two linear equations in two unknowns, i.e., the specific energy of crack formation and specific energy of crack growth. The determined specific energy values are then used to calculate the work of crack nucleation and work of crack growth. The use of the analytical method improves the accuracy compared to graphical - extrapolative procedures. The novelty of the method consists in using one and the same form of the notch in test samples, thus providing the same conditions of the stress-strain state for crack nucleation and growth. Moreover, specimens with different cross-section dimensions are used to eliminate the scale effects. Since the specific energy of the crack nu-cleation and specific energy of the crack growth are independent of the scale factor, they are determined only by the properties of the metal. Introduction the specific energy of crack formation and growth makes possible to assign a specific physical meaning to the fracture energy.

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