Question

Create a function x=backsub(U,y) in matlab that accepts as input

arguments a nxn matrix U and n-vector y, and returns as output a column vector x

consisting of the values of the unknowns x1; x2; : : : ; xn.

Answer 1

function X = backsub(U,y)

%Input - U is an N x N nonsingular matrix

% - y is an N x 1 matrix

%Output - X is an N x 1 matrix containing the solution to UX=y.

%Initialize X and the temporary storage matrix C

[N N]=size(U);

X=zeros(N,1);

C=zeros(1,N+1);

%Form the augmented matrix: Aug=[U|y]

Aug=[U y];

for p=1:N-1

%Partial pivoting for column p

[Q,j]=max(abs(Aug(p:N,p)));

%Interchange row p and j

C=Aug(p,:);

Aug(p,:)=Aug(j+p-1,:);

Aug(j+p-1,:)=C;

  

if Aug(p,p)==0

'U is singular. No unique solution'

break

end

%Elimination process for column p

for k=p+1:N

m=Aug(k,p)/Aug(p,p);

Aug(k,p:N+1)=Aug(k,p:N+1)-m*Aug(p,p:N+1);

end

end

X=backsub(Aug(1:N,1:N),Aug(1:N,N+1));