Linear Systems – Iterative methods Jacobi Method

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Linear Systems Iterative methods Jacobi Method Gauss-Siedel Method 1 Iterative Methods Iterative methods can be expressed in the general form: x(k) F(x(k-1)) where s s.t. F(s)s is called a Fixed Point Hopefully: x(k) s (solution of my

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01
Linear Systems – Iterative methods Jacobi Method
Gauss-Siedel Method 1<br>
02
Iterative Methods Iterative methods can be expressed in the general form: x(k) =F(x(k-1))
where s s.t. F(s)=s is called a Fixed Point

Hopefully: x(k)  s (solution of my problem)

Will it converge? How rapidly? 2<br>
03
Iterative Methods Stationary:
x(k+1) =Gx(k)+c
where G and c do not depend on iteration count (k)

Non Stationary:
x(k+1) =x(k)+ak p(k)
where computation involves information that change at each iteration 3<br>