Question

For the following two problems, use the built-in simple MATLAB matrix algebra rules, i.e. if you're multiplying a matrix L by a vector xi, it's just L*xi. You do not have to code matrix multiplication in for loops.

• Code up the Jacobi Method and use it to solve the large matrix of problem 3 from HW5. Return the iteration count to solve this problem and a plot of the solution.
• Modify the Jacobi method to use the most current information (i.e. implement the Gauss-Seidel method) and solve problem 3 of HW5 once more. Again include the iteration count and solution plot.

Regarding convergence, I suggested examining the norm of the x vector (norm is the MATLAB function name). This could be absolute change in the form norm(x1-x0) (current iteration minus previous iteration); or relative change in the form norm(x1-x0)/norm(x0). These require different error thresholds (i.e. stopping criteria for the iterative loop) for good convergence.

Help with the code for this please. I can use the code to apply it to the problem from HW 5. just need the as much of the code as possible plsssssss

Answer 1

`Hey,

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

clc%clears screen
clear all%clears history
close all%closes all files
format long
A=randi([3,8],10,10);
b=randi([3,8],10,1);
jacobi(A,b,ones(10,1),1e-4,100)
function x = jacobi(A,d,x0,tol,Imax)   
% jacobi: 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.
E=[];
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
b=zeros(n,1);
C=zeros(n,n);
k=0;
for i=1:n
b(i)=d(i)/A(i,i);
end
for i=1:n
for j=1:n
if i==j, C(i,j)=0; end
if i~=j, C(i,j)=A(i,j)/A(i,i); end
end
end
while true
x_old=x;
x=b-C*x;
k=k+1;
E(k)=norm((x-x_old)./x);
if k>=Imax || norm((x-x_old)./x)<tol
fprintf('Total Iterations are: %d\n',k);
plot(E);
return
end
end
end

Note: Brother According to Chegg's policy we are only allowed to answer first part if there are many. So, I request you to post other part as separate posts.

Kindly revert for any queries

Thanks.