GAUSS SEİDAL METHOD İNPUT

    function gauss_seidel_iterasyonu 
clc;clear all;warning off;
A=[5 1 2;2 -4 1;1 -1 -3];b=[15;11;-6]; 
%  A=[4 1 0 0 0 0 0; 1 4 1 0 0 0 0;0 1 4 1 0 0 0; 0 0 1 4 1 0 0; 0 0 0 1 4 1 0; 0 0 0 0 1 4 1 ; 0 0 0 0 0 1 4];
%  b=[ 5;6;6;6;6;6;5]; 
 [n m]=size(A); 
 L=tril(A,-1);U=triu(A,1);D=diag(diag(A)) ;
 x0=zeros(n,1);x1=x0;%başlangıç iterasyonu
 Nit=1000; % maksimum iterasyon 
 %%%%1.yol%%%%% 
 tic
 for k=1:Nit 
     x1=inv(D)*(b-L*x1-U*x0);  
     if norm(x1-x0)<eps     
         break    
     else       
         x0=x1;   
         if k==Nit   
             disp('Yakınsak değildir')    
         end     
     end
 end 
 toc
 fprintf('%5s %3s\n','Çözüm','-x-');
 fprintf('%12.8f\n',x1)
 fprintf('İterasyon %6.0f\n', k)
 x0=zeros(n,1);x2=x0;%başlangıç iterasyonu
 %%%%2.yol%%%%% 
 tic
 for k=1:Nit  
     for i=1:n  
         x2(i)=(b(i)-A(i,1:i-1)*x2(1:i-1)-A(i,i+1:n)*x0(i+1:n))/A(i,i);   
     end   
     if norm(x2-x0)<eps   
         break   
     else       
         x0=x2;  
         if k==Nit 
             disp('Yakınsak değildir')  
         end   
     end
 end 
 toc 
 fprintf('%5s %3s\n','Çözüm','-x-');
 fprintf('%12.8f\n',x2)
 fprintf('İterasyon %6.0f\n', k) 
    end

HOW CAN I INPUT THE INPUT OF A- B AND ITERATION COMMANDS IN THE GAUSS SEİDAL METHOD GIVEN IN THE CODE, CAN YOU HELP? I would be very pleased if you could send it as a direct code.

[Torsten]

A, b and Nit are prescribed at the beginning of the code. You can change them there. Or you can call the function with input arguments A, b and Nit and comment out the lines where they are set.

I recommend also to make "eps" a variable to be prescribed.

Answer 1

[Ravi]

Hi Ömer Faruk Parlak,

I assume you are facing an issue in providing matrix input to the Gauss Siedel method dynamically instead of hardcoding the matrices.

Observe the following cases, low dimension matrices and large matrices.

In case of low-dimension matrices, the user can read the entries of the matrices interactively by prompting on the screen.

rows = input('Enter the number of rows: '); 
cols = input('Enter the number of columns: '); 

% Initialize the matrix with zeros 
matrix = zeros(rows, cols); 

% Prompt the user to enter the matrix elements row by row 
for i = 1:rows 
    for j = 1:cols 
        prompt = sprintf('Enter the element at (%d, %d): ', i, j); 
        matrix(i, j) = input(prompt); 
    end 
end 

In case of large matrices, it would be difficult to read the matrix by prompting to the screen. In such cases, we can load the matrix from a text file, csv file, or a mat file.

Let us assume the matrix is present in a file named “data.txt”, then we can read the matrix as follows.

matrix = load('data.txt'); 

If the matrix is present in a .mat file, then we can input the matrix as follows.

% Assume 'data.mat' is a MATLAB file containing a variable 'A' which is the matrix 
load('data.mat', 'matrix'); 

After the matrix input, number of iterations can be taken as input using the “input” function.

To learn more about the above-mentioned functions, please refer to the following links.

input – https://www.mathworks.com/help/matlab/ref/input.html

load - https://www.mathworks.com/help/matlab/ref/load.html

Hope this explanation clears the issue you are facing.

Thanks,

Ravi Chandra