MATLAB PLEASE MATLAB PLEASE PLEASE SOLVE ONLY b a) Develop a program using a lib

Question

MATLAB PLEASE

MATLAB PLEASE

PLEASE SOLVE ONLY b a) Develop a program using a library or a package of your choice for Gauss Seidel Method with x(0)-0 to approximate the solution to the given linear system with an error tolerance ?,-10-3 in the maximum magnitude norm (1X10) 4x +x2-3+x2 PLEASE SOL xi + 4x2-X3-X4 =-1 -xi-x2 +5x3 +x4=0 xi-x2 +x3 +3x4 =1 PLEASE SOLVE ONLY b 4x1 + x2-x3 + x4 =-2 b) Solve the same set of equations with the same initial conditions and error tolerance using SOR Method with w= 1.1.

Explanation / Answer

%for SOR method

function x = SOR( A ,B )

disp ( ' Enter system of equations in the form of AX=B')

% Calling matrix A

A = input ( ' Enter matrix A :   ')

% check for matrix A

% it should be a square matrix

[na , ma ] = size (A);

if na ~= ma

    disp('ERROR:matrix A should be a square matrix')

    return

end

% calling matrix B

B = input ( ' Enter matrix B :   ')

% check for matrix B

[nb , mb ] = size (B);

if nb ~= na || mb~=1

   disp( 'ERROR:input error..pls re-enter data')

   return

end

w=input('Enter the relaxation parameter   ');

% A = D + L + U

D = diag(diag(A));

L = tril(A)- D;

U = triu(A)- D;

% check for convergence of system

e= max(eig(inv( D+w*L) * ( D*(1-w) - w*U)));

if abs(e) >= 1

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

    disp ('This process is not convergent. Please try some other process.')

    return

end

% initial guess for X..?

% default guess is [ 1 1 .... 1]'

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

switch r

    case 'y'

        % asking for initial guess

    X0 = input('pls enter initial guess for X : ')

        % check for intial guess

    [nx, mx] = size(X0);

    if nx ~= na || mx ~= 1

        disp( 'ERROR: pls check input')

        return

    end

    otherwise

    X0 = ones(na,1);

end

%allowed error in final answer

t = input ( 'enter the error allowed in final ans:  ');

tol = t*ones(na,1);

k= 1;

X( : , 1 ) = X0;

err= 1000000000*rand(na,1); %intial error assumtion for looping

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

    X ( : ,k+ 1 ) = inv(D+w*L) * ( D*(1-w) - w*U)*X( : ,k) + inv(D+ w*L)*B;% SOR formula

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

    k = k + 1;

    

end

fprintf (' The final ans obtaibed after %d itaration which is   ', k)

X( : ,k)

While giving input to the program, the standard MATLAB syntaxes must be obeyed. Here’s a sample output of the MATLAB program for SOR method:

Matrix A = [4 1-1 1;1 4 -1 -1;-1 -1 5 1; 1 -1 1 3]

Matrix B= [-2 -1 0 1]

Enter the relaxation paramter = 1.1

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