Jacobi method

From CFD-Wiki

We seek the solution to set of linear equations:

For the given matrix A and vectors X and Q.
In matrix terms, the definition of the Jacobi method can be expressed as :

Where D,L and U represent the diagonal, lower triangular and upper triangular matrices of coefficient matrix A and k is iteration counter.

Algorithm

Chose an intital guess to the solution

for k := 1 step 1 untill convergence do

for i := 1 step until n do

for j := 1 step until n do

if j != i then

end if

end (j-loop)

end (i-loop)

check if convergence is reached

end (k-loop)

Note: The major difference between the Gauss-Seidel method and Jacobi method lies in the fact that for Jacobi method the values of solution of previous iteration (here k) are used, where as in Gauss-Seidel method the latest available values of solution vector X are used.

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