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  2. Gauss–Seidel method - Wikipedia

    en.wikipedia.org/wiki/Gauss–Seidel_method

    Gauss–Seidel method. 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, and is similar to the Jacobi ...

  3. Tridiagonal matrix algorithm - Wikipedia

    en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm

    Tridiagonal matrix algorithm. In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas ), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as.

  4. Conjugate gradient method - Wikipedia

    en.wikipedia.org/wiki/Conjugate_gradient_method

    Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2). In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite.

  5. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. [1] For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously ...

  6. Gaussian elimination - Wikipedia

    en.wikipedia.org/wiki/Gaussian_elimination

    In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of ...

  7. Differential-algebraic system of equations - Wikipedia

    en.wikipedia.org/wiki/Differential-algebraic...

    e. In mathematics, a differential-algebraic system of equations ( DAE) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. The set of the solutions of such a system is a differential algebraic variety, and corresponds to an ideal in a differential algebra of ...

  8. Successive over-relaxation - Wikipedia

    en.wikipedia.org/wiki/Successive_over-relaxation

    Successive over-relaxation. In numerical linear algebra, the method of successive over-relaxation ( SOR) is a variant of the Gauss–Seidel method for solving a linear system of equations, resulting in faster convergence. A similar method can be used for any slowly converging iterative process .

  9. Jacobi method - Wikipedia

    en.wikipedia.org/wiki/Jacobi_method

    Jacobi method. In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges.