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# Jacobi method

In numerical linear algebra, the Jacobi method (or Jacobi iterative method) is an algorithm for determining the solutions of a diagonally dominant system of linear equations. [1]

## Carl Gustav Jacob Jacobi

Carl Gustav Jacob Jacobi (10 December 1804 – 18 February 1851) was a German mathematician, who made fundamental contributions to elliptic functions, dynamics, differential equations, and number theory.

## Diagonal matrix

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero.

## Diagonally dominant matrix

In mathematics, a square matrix is said to be diagonally dominant if for every row of the matrix, the magnitude of the diagonal entry in a row is larger than or equal to the sum of the magnitudes of all the other (non-diagonal) entries in that row.

## 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 linear system of equations.

## Jacobi eigenvalue algorithm

In numerical linear algebra, the Jacobi eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric matrix (a process known as diagonalization).

## Johns Hopkins University

Johns Hopkins University is an American private research university in Baltimore, Maryland.

## Matrix splitting

In the mathematical discipline of numerical linear algebra, a matrix splitting is an expression which represents a given matrix as a sum or difference of matrices.

## Numerical linear algebra

Numerical linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers.

## Phys.org

Phys.org is a science, research and technology news aggregator where much of the content is republished directly from press releases and news agencies-in a practice known as churnalism.

## Positive-definite matrix

In linear algebra, a symmetric real matrix M is said to be positive definite if the scalar z^Mz is strictly positive for every non-zero column vector z of n real numbers.

## Society for Industrial and Applied Mathematics

The Society for Industrial and Applied Mathematics (SIAM) is an academic association dedicated to the use of mathematics in industry.

In mathematics, the spectral radius of a square matrix or a bounded linear operator is the largest absolute value of its eigenvalues (i.e. supremum among the absolute values of the elements in its spectrum).

## 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.

## System of linear equations

In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables.

## References

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