Gauss Seidel Iretative Method

Hello,

I am a structural engineer and our matrices consist of many 0s. Below is my code for using the Gauss seidel method to solve my matrix formula but I am having trouble when dividing by A(i,i) when A(i,i) is 0.

s = ft_GaussSeidel(A,b)

clear all; close all; clc;

A = [.707    1    0    0    0    0    0    0    0    0    0    0    0;
     -.707   0    1    0    0    0    0    0    0    0    0    0    0;
     .7071   0    0    1    0    0    0    0    0    0    0    0    0;
        0   -1    0    0 .659    1    0    0    0    0    0    0    0;
        0    0    0   -1 -.753   0    0    0    0    0    0    0    0;
        0    0   -1    0 -.659   0    1    0    0    0    0    0    0;
        0    0    0    0 .753    0    0    1    0    0    0    0    0;
        0    0    0    0    0   -1    0    0 .659    1    0    0    0;
        0    0    0    0    0    0    0   -1 -.753   0    0    0    0;
        0    0    0    0    0    0   -1    0 -.659   0    1    0    0;
        0    0    0    0    0    0    0    0 .735    0    0    1    0;
        0    0    0    0    0    0    0    0    0   -1    0    0 .707;
        0    0    0    0    0    0    0    0    0    0    0   -1 -.707];
b = [0; 
     2000; 
     -6229; 
     0; 
     600; 
     0; 
     0; 
     0; 
     800; 
     0; 
     2429; 
     0; 
     600];

k = 0; % iteration counter
x_prev = ones(size(b)); % temporary x
x = ones(size(b))*2; % x array (start with 2 not 0s)

% table headings output
count = zeros(size(x));
fprintf('  k| ')
for i = 1:size(x)
    count(i) = i;
    fprintf('%-1c%-10s', 'x', num2str(count(i)))
end

%Calculation code
for k = 1
    x_prev = x; % for checking when iteration should end
    for i = 1:2 %:length(x) % row loop

          %x(i) calculation loops
          x(i) = b(i);
          for ii = 1:length(x) % column loop
              if ii ~= i % does not use column of x(i)
%%%%%%DivBy0Error%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%x(i) = x(i)-A(i,ii)*x(ii) 
              end
          end
          x(i) = x(i)/A(i,i); 
      end

fprintf('\n %2g|',k);
fprintf(' %-10.2e',x);
end

% end
For example the calculation for x2 would be:
x2 = (b2 +.7071*x1)/A(i,i)  | A(i,i) = 0

Would my only option be to make a code to get the diagonals of the matrix to be non-zero? Or can I do something to this?

Answer 1

[Meysam Mahooti]

The Gauss–Seidel method is an iterative technique for solving a square system of n linear equations with unknown x.

https://www.mathworks.com/matlabcentral/fileexchange/73488-gauss-seidel-iterative-method