China
Africa
Explore chapters and articles related to this topic
Linear Algebra
Published in Richard L. Shell, Ernest L. Hall, Handbook of Industrial Automation, 2000
Gaussian elimination is a strategy for solving a system of linear equations. To find all solutions to the linear system of equations () a11x1+a12x2+⋯+a1nxn=b1⋮am1x1+am2x2+⋯+amnxn=bm
Mathematical Concepts in Kinematics
Published in Kevin Russell, Qiong Shen, Raj S. Sodhi, Kinematics and Dynamics of Mechanical Systems Implementation in MATLAB® and Simmechanics®, 2018
Kevin Russell, Qiong Shen, Raj S. Sodhi
A linear equation is an equation that includes linear or first-order variables.* A system of linear equations (or a linear system) is collection of linear equations including the same variables. If a common solution is sought among a system of linear equations, it is called a set of simultaneous equations. An arbitrary set of linear simultaneous equations is given in Equation 2.22. Variables x1, x2, x3, and x4 are included among the four linear equations and true x1, x2, x3, and x4 solutions for these simultaneous equations must satisfy each equation in the set.
Linear Algebra
Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012
Fatemeh Hamidi Sepehr, Erchin Serpedin
In general, a system of linear equations might admit either a single solution, infinitely many solutions, or no solution. In the literature, there have been proposed a large number of approaches to calculate the solution of a linear system of equations. Among the most encountered approaches, one can resort to the variable elimination (or substitution) method, reduction to row echelon form method, Cramer's rule, various factorization approaches (such as the LU decomposition or Cholesky factorization), and iterative approaches (see e.g., [5, 7] for a review of these approaches). In what follows, we will review some of the most important concepts and factorizations pertaining to matrices.
Electrical magneto hydrodynamic Jeffrey fluid flow with thermal radiation through stretched cylinder
Published in Waves in Random and Complex Media, 2022
Kotha Gangadhar, M. Prameela, Konduru Bhanu Lakshmi, Ali J. Chamkha
Since no further variation is observed after increasing the number of elements (n) 660 and 360,500, the flow field is divided into 500 quadratic parts of equal size (Table 1). We can estimate three functions of order 2505 × 2505 are obtained after assembling all particle equations. The resultant matrix is nonlinear after applying boundary conditions (Equations 31–32), which is solved using the N–R technique with the required precision of 0.00005. The Gauss elimination method is used to solve a system of linear equations (see Figure 1).
Linear Algebra on Parallel Structures Using Wiedemann Algorithm to Solve Discrete Logarithm Problem
Published in IETE Journal of Research, 2022
K S Spoorthi, R. Padmavathy, S K Pal, S Ravi Chandra
Gaussian Elimination is the oldest available algorithm to solve the system of linear equations. Gaussian elimination reduces the matrices to row echelon form, then solves the system of linear equations. For a matrix M of size , the complexity of the method can be given by or . The complexity is too high for large matrices. It does not utilize the sparsity of the matrix. Hence FFS does not use Gaussian Elimination.