For this problem, you don\'t really need to write a MATLAB generalized function

Question

For this problem, you don't really need to write a MATLAB generalized function to calculate the solution for a system for equations using Gauss Seidel method (If you can that's even better). What you can alternatively do is solve the three equations in problem 1 for x1, x2, and x3 and put them within a for loop. You can create dummy variables to store the previous iteration values of x1, x2, and x3 to calculate the error. Write a user-defined MATLAB function that solves a system of n linear equations, [a][x] = [b], with the Gauss-Seidel method. For the function name and arguments use x = Gauss Seidel(a, b), where a is the matrix of coefficients, b is the right-hand-side column of constants, and x is the solution. Use Gauss Seidel to solve problems 1. This is problem 1 as a reference, but solve problem 4. Carry out the first three iterations of the solution of the following system of equations using the Gauss Seidel iterative method For the first guess of the solution, take the value of all the unknowns to be zero. 8x_1 + 2x_2 + 3x_3 = 51 2x_1 + 5x_2 + x_2 + 6x_3 = 20

Explanation / Answer

(4).function x=GaussSeidel(A,b,y,N) %% method for gaussseidel

D=diag(A); %% diagnol

A=A-diag(D);

%% inverse

D=1./D;

%%length

n=length(y);

y=y(:);

x=zeros(n,NumIters);

for j=1:NumIters

for k=1:n

x(k)=(b(k)-A(k,:)*x)*D(k);

end

y(:,j)=y;

end

1Ans:Enter the matrix as 8 2 3 51

2 5 1 23

-3 1 6 20

follow the code

function x = gauss_siedel( A ,B )

disp ( 'Input linear equations in the form of AX=B')

%Input matrix A

A = input ( 'input matrix A : ')

% check if the entered matrix is a square matrix

[na , ma ] = size (A);

if na ~= ma

disp('ERROR: Matrix A must be square matrix') %% square matrix only

return

end

% Input matrix B

B = input ( 'Enter matrix B : ')

[nb , mb ] = size (B);

if nb ~= na || mb~=1

disp( 'ERROR: Matrix B must be column matrix') %% must be column matrix

return

end

% A = D + M + U

D = diag(diag(A));

L = tril(A)- D;

U = triu(A)- D

e= max(eig(-inv(D+M)*(U)));

if abs(e) >= 1

disp ('Since the modulus of the largest Eigen value of iterative matrix is not less than 1')

disp ('this process is not convergent.')

return

end

  

r = input ( 'Any initial guess for X? (y/n): ','s');

switch r

case '1'

X0 = input('Enter initial guess for X : ')

% check for initial guess

[nx, mx] = size(X0);

if nx ~= na || mx ~= 1

disp( 'ERROR: Check input')

return

end

otherwise

X0 = ones(na,1);

end

  

t = input ( 'Enter the error allowed in final answer: ');

tol = t*ones(na,1);

k= 1;

X( : , 1 ) = X0;

err= 1000000000*rand(na,1);% initial error assumption for looping

while sum(abs(err) >= tol) ~= zeros(na,1)

X ( : ,k+ 1 ) = -inv(D+M)*(U)*X( : ,k) + inv(D+M)*B; %%its Gauss Seidel formula

err = X( :,k+1) - X( :, k);%%for find error

k = k + 1;

  

end

fprintf ('The final answer after %g iterations is ', k)

X( : ,k)

end

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