Use MATLAB for this assignment Please follow the steps and write your code clear

Question

Use MATLAB for this assignment
Please follow the steps and write your code clearly Due Sun 10/29, 11pm Implement algorithm 6.1 that accomplishes Gaussian elimination with row swap ping. INPUT mllmler of unknowns n; and the argument matrix A = layl, where OUTPUT: solation Step 1: For i- 1 to n-1 do steps 2-4 Step 2: Let p be the smallest integer with i p n and Spi0. If no integer p can be found then output (no uniqae solution') STO Step 3: If then perform swap the p-th row and i-th row Step 4: For j =i+1, nclo steps 5 and 6 Step 5:Set m-aa Step 6: Perform (E,-my,E,) E, where E, represents j-th row orj-th equation Step 7: If athen OUTPUT('no unique solation exists): STOP Step 8: Set zn =@n,n+1/amn. Step 9; For i-n-1, ISet z.-lai,n+1 _ ..+1@yz,] /@w Step 10 OUTPUT (zi,Z2, z"). STOP Use the above algorithm to solve the system of equations

Explanation / Answer

Matlab function GaussianElimination_Row_Swaping.m

function x = GaussianElimination_Row_Swaping(A)
% Matlab program to solve system of equation using Gaussian Elimination
% with row swaping
[n1,n2] = size(A); % Get the size of the input array
x = zeros(1,n1); % initilizing the solution vector
for i = 1:n1 -1 % Step 1 For i = 1 to n-1 do step 2 - 4
    % Step 2: let p be the smallest integer with i<= p<= n and A(p,i) != 0
    p = i;
    while(A(p,i)== 0 && p<= n1)
        p = p+1;
    end
    % if no integer can be found then output no unique solution
    if p > n1
        fprintf('No unique solution ');
        return;
    end
    % Step 3: id p!= i then interchange pth and ith row
    if p~=i
        T = A(p,:);
        A(p,:) = A(i,:);
        A(i,:) = T;
    end
    % Step 4: For j = i+1 to n fo step 5 and 6
    for j = i+1:n1
        % Step 5: set m(j,i) = a(j,i)/a(i,i)
        m(j,i) = A(j,i)/A(i,i);
        % Step 6: Perform Aj = (Aj-m(j,i)*Ai)
        A(j,:) = A(j,:)-m(j,i)*A(i,:);
    end
end
% Step 7: if a(n,n) is zero print No unique solution
if A(n1,n1) == 0
    fprintf('No unique solution ');
    return;
end
% Step 8: set xn = a(n,n+1)/a(n,n)
x(n1) = A(n1,n2)/A(n1,n1);
% Step 9: for i = n-1 to 1 set x xi = 9a(i,n+1) - sum j - i+1 to n
% a(i,j)*x(j))/a(i,i)
for i = n1-1:-1:1
    sum = 0;
    for j = i+1:n1
        sum = sum + A(i,j)*x(j);
    end
    x(i) = (A(i,n2)-sum)/A(i,i);
end
% Step 10: solution is in x
end

Calling the function

>> A = [pi -2^0.5 -1 1 0;
        eps -1 1 2 1;
        1 1 -3^0.5 1 2;
        -1 -1 1 -5^0.5 3];
>> x = GaussianElimination_Row_Swaping(A)

x =

   -6.4507   -7.5028   -8.6042    1.0507

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.