%%%%%%%%%% Note: Problem 1 you have not given so I have taken one example problem
function xrt=gaus_jocob_Sidel()
clc;
clear all;
% 10x1 + x2 - x3 = 18
%
% x + 15x2 + 2x3 = -12
%
% -x1 + x2 + 20x3 = 17
A = [6 -1 2 1 ; 1 6 1 -1;0 1 3 1;1 -2 1 5];
b = [3; 2; -6;1];
n=length(b);
% error tolerance
disp('Exact solution by Matirx inverse')
y=inv(A)*b %%%Exact
%initial guess:
x0 = ones(n,1);
tol=1e-6; % Stoping (tolerence)
iter=1;
disp(' Solution, number of iteration and error by Gauss Jacobi
method')
[x_jacobian, iter, err1]=gausjocobi(A,b,x0,tol)
disp(' Solution, number of iteration and error by Gauss Seidel
method')
[x_gauss, iter, err1]=gausssidel(A,b,x0,tol)
% [x_Sor, iter]=Sor(A,b,x0,tol)
function [x_jacobian, iter, err1]=gausjocobi(A,b,x0,tol)
% Jacobi method
%---------------
%A is matrx
%b is right side matrix
%x0 is inital vector
%tol is tolerence
xnew=x0;
iter=1;
error=1;
while (error>tol )
xold=xnew;
for i=1:length(xnew)
off_diag = [1:i-1 i+1:length(xnew)];
xnew(i) = 1/A(i,i)*( b(i)-sum(A(i,off_diag)*xold(off_diag))
);
end
error=norm(xnew-xold);
err1(iter)=error;
iter = iter+1;
end
x_jacobian=xnew;
end
function [x_gauss, iter, err1]=gausssidel(A,b,x0,tol)
xnew=x0;
iter=1;
err=1;
while (err>tol)
lambda=1;
xold=xnew;
for i=1:n
I = [1:i-1 i+1:n];
xnew(i) = (1-lambda)*xnew(i)+lambda/A(i,i)*( b(i)-A(i,I)*xnew(I)
);
end
err = norm(xnew-xold);
err1(iter)=err;
iter = iter+1;
end
x_gauss=xnew;
end
end
%%%%%%%% Solution
Exact solution by Matirx inverse
y =
1.305429864253394
0.635746606334842
-2.438914027149322
0.680995475113122
Solution, number of iteration and error by Gauss Jacobi method
x_jacobian =
1.305429958624094
0.635746583563940
-2.438914093841731
0.680995535312764
iter =
16
err1 =
Columns 1 through 3
3.933615809065920 1.574193895221642 0.486147264969486
Columns 4 through 6
0.175559380981398 0.056338328280127 0.019173026432052
Columns 7 through 9
0.006157919146378 0.002042336090436 0.000629963356748
Columns 10 through 12
0.000208036056003 0.000059033489543 0.000019697795727
Columns 13 through 15
0.000004870769552 0.000001681352088 0.000000334066886
Solution, number of iteration and error by Gauss Seidel method
x_gauss =
1.305429870055986
0.635746615687181
-2.438914040669446
0.680995480397565
iter =
12
err1 =
Columns 1 through 2
3.609349522843711 1.127507478402957
Columns 3 through 4
0.094708804346742 0.016763100058599
Columns 5 through 6
0.005555852012273 0.001033868860446
Columns 7 through 8
0.000112855725824 0.000015284172615
Columns 9 through 10
0.000005320753452 0.000001066916329
Column 11
0.000000125915926
>>
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