Iterative method used to solve a linear system of equations
Not to be confused with Jacobi eigenvalue algorithm.
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. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
In numerical linear algebra, the Jacobimethod (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly...
Jacobi may refer to: People with the surname Jacobi Mathematics: Jacobi sum, a type of character sum Jacobimethod, a method for determining the solutions...
Carl Gustav Jacob Jacobi (/dʒəˈkoʊbi/; German: [jaˈkoːbi]; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions...
In numerical linear algebra, the Jacobi eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric...
mathematics, the Jacobimethod for complex Hermitian matrices is a generalization of the Jacobi iteration method. The Jacobi iteration method is also explained...
The Jacobimethod can be represented in matrix form as a splitting The Gauss–Seidel method can be represented in matrix form as a splitting The method of...
Friedrich Heinrich Jacobi (German: [jaˈkoːbi]; 25 January 1743 – 10 March 1819) was an influential German philosopher, literary figure, and socialite....
methods would not reach the solution within a finite number of steps (in general). Examples include Newton's method, the bisection method, and Jacobi...
for y with x fixed. Rather than iterate until convergence (like the Jacobimethod), the algorithm proceeds directly to updating the dual variable and...
of the iterative methods. One example of an iterative method is the Jacobimethod, where the matrix A {\displaystyle A} is split into its diagonal component...
Hamilton–Jacobimethod, in which solutions to Hamilton's equations are sought by first finding a complete solution of the associated Hamilton–Jacobi equation...
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see...
The Jacobi symbol is a generalization of the Legendre symbol. Introduced by Jacobi in 1837, it is of theoretical interest in modular arithmetic and other...
Jacobi Medical Center (NYC Health + Hospitals/Jacobi) is a municipal hospital operated by NYC Health + Hospitals in affiliation with the Albert Einstein...
shown to converge faster than classical iterative methods like the Jacobimethod, the Gauss–Seidel method, successive over-relaxation, and others. Additionally...