Description
Given a square system of n linear equations:
where:
Then A can be decomposed into a diagonal component D, and the remainder R:
The solution is then obtained iteratively via
The element-based formula is thus:
Note that the computation of xi(k+1) requires each element in x(k) except itself. Unlike the Gauss–Seidel method, we can't overwrite xi(k) with xi(k+1), as that value will be needed by the rest of the computation. The minimum amount of storage is two vectors of size n.
Read more about this topic: Jacobi Method
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