Question

A) Use Jacobi or Gauss-Seidel iteration and perform three iterations by hand.

B) Use Jacobi or Gauss-Siedel iteration for ten iterations with a MAT-LAB function.

* A= [5, -1,0;-1,5,-1;0,-1,5] , B=[9;4;-6]

Answer 1

unalim 6+116 ly 1.LG -0.96&

- 96 1. 12 6 + 5 6 50

Code

A=[5 -1 0;-1 5 -1;0 -1 5];
b=[9;4;-6];
x=[0;0;0];
format long

for k=1:10
   disp('iteration')
   disp(k)
for i=1:3
        sum=0;
        sum=sum+b(i);
    for j=1:3
        if i==j
            sum=sum;
        else
            sum=sum-A(i,j)*x(j);
        end
       
    end
    sum=(1/A(i,i))*sum;
    x(i)=sum;
  
    end
    x
end

Output

>gaussseiedel iteration 1.800000000000000 1.160000000000000 0.968000000000000 iteration 2 2.032000000000000 1.012800000000000 0.997440000000000 iteration 2.002560000000000 1.001024000000000 0.999795200000000 iteration 4 2.000204800000000 1.000081920000000 0.999983616000000 iteration 2.000016384000000 1.000006553600000 0.999998689280000

iteration 2.000001310720000 1.000000524288000 0.999999895142400 iteration 2.000000104857600 1.000000041943040 0.999999991611392 iteration 2.000000008388608 1.000000003355443 0.999999999328911 iteration 2.000000000671089 1.000000000268436 0.999999999946313 iteration 10 2.000000000053687 1.000000000021475 0.999999999995705