JACOBI METHOD

THE JACOBI METHOD

The Jacobi method is easily derived by examining each of the equations in the linear system Ax = b in isolation.

The Jacobi method is based on solving for every variable locally with respect to the
other variables; one iteration of the method corresponds to solving for every variable once. The resulting method is easy to understand and implement, but convergence is slow.

Jacobi method belongs to the category of so-called stationary iterative methods. These methods can be expressed in the simple form x(k) = Fx(k−1) + c, where
x(k) is the approximation to the solution vector at the k-th iteration and neither F nor c depend on k.

The Jacobi method does not converge for all linear equation systems. In such cases, Jacobi may be made to converge by introducing an under-relaxation parameter
in the standard Jacobi. Furthermore, it may also be possible to accelerate the convergence of the standard Jacobi method by using an over-relaxation parameter.
The resulting method is known as Jacobi overrelaxation (JOR) method.


Jacobi Method