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The tridiagonal matrix algorithm, also known as the Thomas algorithm, is a simplified form of Gaussian elimination for solving tridiagonal systems of equations. Learn the method, derivation, variants and examples of this numerical linear algebra technique.
In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel .
Gaussian elimination is an algorithm for solving systems of linear equations by performing row operations on the coefficient matrix. It is named after Carl Friedrich Gauss and can also compute the rank, determinant and inverse of a matrix.
Learn about the definition, examples, and solution methods of a system of linear equations, a collection of two or more linear equations involving the same variables. Explore the geometric interpretation, the general form, and the behavior of linear systems in different cases.
A method for solving linear systems of equations faster by using a relaxation factor. Learn the formulation, convergence rate, algorithm and example of this numerical linear algebra technique.
LU decomposition is a matrix factorization that factors a square matrix into a lower triangular matrix and an upper triangular matrix. It is used in numerical analysis and linear algebra to solve systems of linear equations, invert matrices, and compute determinants.
The Jacobi method is an iterative algorithm for solving a strictly diagonally dominant system of linear equations. It involves solving each diagonal element for and updating the approximation until convergence. See examples, convergence conditions, and Python code.
Thus solving a polynomial system over a number field is reduced to solving another system over the rational numbers. For example, if a system contains 2 {\displaystyle {\sqrt {2}}} , a system over the rational numbers is obtained by adding the equation r 2 2 – 2 = 0 and replacing 2 {\displaystyle {\sqrt {2}}} by r 2 in the other equations.
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