Jacobi_Method

Solution of system of linear equations

An iterative method to solve a system of linear equations, AX = B.

A general linear iterative method for the solution of the system of
linear equations is defined as :
X^(k+1) = H*X^(k) + c where k = 0,1,2... and
X^(k+1) and X^(k)) are the (k+1)th and kth iterations for X.
H is called the iteration matrix.

In the limiting case when k -> ∞, X^(k) converges to the exact solution. X = A^(-1)B

For Jacobi Iteration Method :-
Assumption : Diagonal entries of coefficient matrix A are pivot elements.
H = -D^-1*(L + U) and
c = D^-1*B where
D is the diagonal matrix, L & U are respectively
lower and upper triangular matrices with zero diagonal entries such that
A = L + D + U