mathlab--jacobi iteration method

how can ı solve this linear system with Gauss-seidel iteration method using mathlab codes??
5x - y + z=10
2x + 8y -z=11
-x + y + 4z=3
ı have some codes but how can ı implement on this question actually ı don't know please somebody help me.i am giving the codes;
function [x,G,c] = gsmp(A,b,n,z)
%
% x = gsmp(A,b,n,z)
%
% Gauss-Seidel iteration on system A*x = b with printing
% using matrix multiplication (not optimal)
% n -- number of iterations
% z -- initial vector (default 0)
%
% x -- final iterate
% G -- Gauss-Seidel matrix
% c -- Gauss-Seidel vector
%

if nargin <=3, z=0*b; end

LD = tril(A);
G = -LD\triu(A,1);
c = LD\b;
x=z;
for i = 1:n
x = G*x + c;
fprintf(1,'%3d ',i)
fprintf(1,'%5.5f ',x')
fprintf(1,'\n')
end

Quote:

---

Originally Posted by sah_mat

how can ı solve this linear system with Gauss-seidel iteration method using mathlab codes??
5x - y + z=10
2x + 8y -z=11
-x + y + 4z=3
ı have some codes but how can ı implement on this question actually ı don't know please somebody help me.i am giving the codes;
function [x,G,c] = gsmp(A,b,n,z)
%
% x = gsmp(A,b,n,z)
%
% Gauss-Seidel iteration on system A*x = b with printing
% using matrix multiplication (not optimal)
% n -- number of iterations
% z -- initial vector (default 0)
%
% x -- final iterate
% G -- Gauss-Seidel matrix
% c -- Gauss-Seidel vector
%

if nargin <=3, z=0*b; end

LD = tril(A);
G = -LD\triu(A,1);
c = LD\b;
x=z;
for i = 1:n
x = G*x + c;
fprintf(1,'%3d ',i)
fprintf(1,'%5.5f ',x')
fprintf(1,'\n')
end

---

Try this:

Code:

---

function [x] = gsmp(A,b,n,z)
%
% x = gsmp(A,b,n,z)
%
% Gauss-Seidel iteration on system A*x = b
%
% n -- number of iterations
% z -- initial vector (default 0)
%
% x -- final iterate
 
 
 
if nargin <=3, z=0*b; end
 
 
L = tril(A);    %lower triangular part of A
U = triu(A);  %upper triangular part of A
D = diag(diag(A));  %diag matrix with same diag as A
 
x=z;
 
for i = 1:n
  x =(D+L)\(b-U*x);
  disp([i,x'])
end

---

with calling code:

Code:

---

A=[5,-1,1;2,8,-1;-1,1,4]
b=[10;11;3]
x=gsmp(A,b,20,[1;1;1]);

---

Reference

CB

first ı want to thank you captain,i have been searching this homework for about a week and recently i tried your code but it gives me an error like this ı don't know what to do;

Code:

---

??? function [x] = gsmp(A,b,n,z)
    |
Error: Function definitions are not permitted at the prompt or in scripts.

---

but ı found another solution,but it is possible that my teacher won't accept it becouse she wants me to write a script and ı really going to be crazy ı have more exams to study whatever ı am givin my solution her check it please;

Code:

---

>> M = [5 -5 1; 2 8 -1; -1 1 4];
b = [10 11 3]';
D = diag( M ).^-1

D =

    0.2000
    0.1250
    0.2500

>> Moff = M - diag( diag( M ) )

Moff =

    0    -5    1
    2    0    -1
    -1    1    0

>> x = [0, 0, 0]'

x =

    0
    0
    0

>> for i = 1:100
    xold = x;

    for j = 1:3
      x(j) = D(j)*(b(j) - Moff(j, :)*x);
    end

    if norm( x - xold ) < 0.001
      break;
    end
end
>> i

i =

    9

>> x

x =

    2.6284
    0.8667
    1.1904

---

Quote:

---

Originally Posted by sah_mat

first ı want to thank you captain,i have been searching this homework for about a week and recently i tried your code but it gives me an error like this ı don't know what to do;

Code:

---

??? function [x] = gsmp(A,b,n,z)
    |
Error: Function definitions are not permitted at the prompt or in scripts.

---

---

You put the function definition in a file called gsmp.m on the search path, or add the directory with it to the search path.

Also if a script file is required you put:

Code:

---

A=[5,-1,1;2,8,-1;-1,1,4]
b=[10;11;3]
x=gsmp(A,b,20,[1;1;1])

---

in a file in the same directory and call it something like script.m and invoke it at the command prompt with:

Code:

---

>>script

---

CB

ı appreciate you captain blac for your helps ı tried your last advice and it realyy works,then ı send it to my teacher she said 'this m.file is too professional probably u did not write it ı want a simple one which u can write'' so ı want u too ask a more question captain ı wrote a solution code at my previous message can we write a gsmp.m file with using the codes in that solution if u help me ı really be glad ı have to study my other exams ı think i am in trouble with the mathlab.THANKS for your helps captain black.

Quote:

---

Originally Posted by sah_mat

ı appreciate you captain blac for your helps ı tried your last advice and it realyy works,then ı send it to my teacher she said 'this m.file is too professional probably u did not write it ı want a simple one which u can write'' so ı want u too ask a more question captain ı wrote a solution code at my previous message can we write a gsmp.m file with using the codes in that solution if u help me ı really be glad ı have to study my other exams ı think i am in trouble with the mathlab.THANKS for your helps captain black.

---

Put this in a script file:

Code:

---

M = [5 -5 1; 2 8 -1; -1 1 4];
b = [10 11 3]';
D = diag( M ).^-1

Moff = M - diag( diag( M ) )

x = [0, 0, 0]'

for i = 1:100
    xold = x;

    for j = 1:3
      x(j) = D(j)*(b(j) - Moff(j, :)*x);
    end

    if norm( x - xold ) < 0.001
      break;
    end
end

disp( i)

disp( x)

---

CB

it is really working thanks a lot CB.ı think ı can implement the same steps for solving with gauss-seidel method.(Clapping)