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Jacobi method information


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.

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Jacobi method

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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...

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Jacobi

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Jacobi may refer to: People with the surname Jacobi Mathematics: Jacobi sum, a type of character sum Jacobi method, a method for determining the solutions...

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Carl Gustav Jacob Jacobi

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Carl Gustav Jacob Jacobi (/dʒəˈkoʊbi/; German: [jaˈkoːbi]; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions...

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Jacobi eigenvalue algorithm

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In numerical linear algebra, the Jacobi eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric...

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Iterative method

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method: M := 1 ω I ( ω ≠ 0 ) {\displaystyle M:={\frac {1}{\omega }}I\quad (\omega \neq 0)} Jacobi method: M := D {\displaystyle M:=D} Damped Jacobi method:...

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Jacobi method for complex Hermitian matrices

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mathematics, the Jacobi method for complex Hermitian matrices is a generalization of the Jacobi iteration method. The Jacobi iteration method is also explained...

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Matrix splitting

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The Jacobi method 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...

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List of things named after Carl Gustav Jacob Jacobi

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method Jacobi method for complex Hermitian matrices Jacobi multiplier Jacobi operator Jacobi polynomials Continuous q-Jacobi polynomials Big q-Jacobi...

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Pidgin code

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gradient method Ford-Fulkerson algorithm Gauss–Seidel method Generalized minimal residual method Jacobi eigenvalue algorithm Jacobi method Karmarkar's...

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Friedrich Heinrich Jacobi

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Friedrich Heinrich Jacobi (German: [jaˈkoːbi]; 25 January 1743 – 10 March 1819) was an influential German philosopher, literary figure, and socialite....

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Numerical analysis

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methods would not reach the solution within a finite number of steps (in general). Examples include Newton's method, the bisection method, and Jacobi...

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Augmented Lagrangian method

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for y with x fixed. Rather than iterate until convergence (like the Jacobi method), the algorithm proceeds directly to updating the dual variable and...

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System of linear equations

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of the iterative methods. One example of an iterative method is the Jacobi method, where the matrix A {\displaystyle A} is split into its diagonal component...

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Integrable system

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Hamilton–Jacobi method, in which solutions to Hamilton's equations are sought by first finding a complete solution of the associated Hamilton–Jacobi equation...

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Jacobi elliptic functions

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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...

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Jacobi symbol

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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...

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Jacobi Medical Center

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Jacobi Medical Center (NYC Health + Hospitals/Jacobi) is a municipal hospital operated by NYC Health + Hospitals in affiliation with the Albert Einstein...

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Belief propagation

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shown to converge faster than classical iterative methods like the Jacobi method, the Gauss–Seidel method, successive over-relaxation, and others. Additionally...

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List of numerical analysis topics

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Iterative methods: Jacobi method Gauss–Seidel method Successive over-relaxation (SOR) — a technique to accelerate the Gauss–Seidel method Symmetric successive...

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