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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.
Learn about the conjugate gradient method, an algorithm for solving linear equations or optimization problems. Find out its derivation, implementation, convergence, and variations.
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.
Learn about the definition, classification, examples and numerical treatment of differential-algebraic systems of equations (DAEs), which are systems of equations that contain both differential and algebraic equations. DAEs are different from ordinary differential equations (ODEs) and have different characteristics and challenges in solving them.
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.
Modified Richardson iteration is an iterative method for solving a system of linear equations. Richardson iteration was proposed by Lewis Fry Richardson in his work dated 1910. It is similar to the Jacobi and Gauss–Seidel method. We seek the solution to a set of linear equations, expressed in matrix terms as =.
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