Question

6 5 - x € 4 CS3010_HW1_Wl15.pdf x + V 7 0 0 file:///C:/Users/Jean/Downloads/CS3010_HW1_W115.pdf of 11 | = Contents o - + Q Fit to page ID Page view | All Read aloud L Add notes E 2 to 3) Given the following set of linear equations X: + 2x2 - xy + x4 = 5 – x; – 2x2 – 3x2 + 2x, = 7 2x, + x2 - x; -5x. =-1 X1 + x2 + x3 + x4 = 10 • Solve using x= A-'b Input: (copy and paste the MATLAB or Scilab command in the following box) 5:53 PM Type here to search o & Ô $ a B. 9 e 2 ☺ ^.om 2018/2019
The exercise given above must be done using Gauss Seidel. This must contain an input and an output. The exercise that is given must be done using the method of Gauss Seidel. It must be tested with matlab. It must contain the input and output.

Answer 1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clc
clear all
close all
format long
A=[1,2,-1,1;-1,-2,-3,2;2,1,-1,-5;1,1,1,1];
b=[5;7;-1;10];
x=gauss_seidel(A,b,[11.6;-5;0;3],1e-4,100)
function x = gauss_seidel(A,d,x0,tol,Imax)
% gauss_seidel: implements the Jacobi iterative method
% for solving a system of linear equations.
% Input: A = square coefficient matrix (nxn)
% d = right hand side vector (nx1)
% x0 = initial guess (nx1) (default = zeros)
% tol = stop criterion (default = 10^-6)
% Imax = maximum iterations (default = 100)
% Output: Solution vector.
if nargin<5, Imax=100; end
if nargin<4, tol=10^-6; end
[m,n]=size(A);
if m~=n, error('Matrix A must be square'); end
if nargin<3, x=zeros(n,1); else x=x0; end
C=A;
for i=1:n
C(i,i)=0;
end
for i=1:n
C(i,1:n)=C(i,1:n)/A(i,i);
end
b=zeros(1,n);
for i=1:n
b(i)=d(i)/A(i,i);
end
iter=0;
while true
x_old=x;
for i=1:n
x(i)=b(i)-C(i,:)*x;
if x(i)~=0
err(i)=abs((x(i)-x_old(i))/x(i));
end
end
iter=iter+1;
if iter>=Imax || norm((x-x_old)./x)<tol
fprintf('Total Iterations are: %d\n',iter);
return
end
end
end

Kindly revert for any queries

Thanks.