学步园

%Program 3.2  (Uppr Triangularization Followed by Back Subtitution)

function X = uptrbk(A,B)

%Input  - A is an N x N nonsingular matrix

%        - B is an N x 1 matrix

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

%Initialize X and the temporary storage matrix C 

[N N]=size(A);

X=zeros(N,1);

C=zeros(1,N+1);

%Form the augmented matrix: Aug=[A|B]

Aug=[A B];

for p=1:N-1

     %Partial pivoting for column p

     [Y,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

      'A was 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

 

%Back Substitution on [U|Y] using Program 3.1

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

Backsub.m

function X=backsub(A,B)

 

%Input  - A is an n x n upper-triangular nonsingular  matrix

%        - B is an n x 1 matrix

%Output - X is the solution to the linear system AX = B

%Find the dimension of B and initialize X

n=length(B);

 X=zeros(n,1);

 X(n)=B(n)/A(n,n);

for k=n-1:-1:1

      X(k)=(B(k)-A(k,k+1:n)*X(k+1:n))/A(k,k);

end

 Untitle.m

A=[

    1 0 0 0 0 0 0

    1 1 1 1 1 1 1

    1 2 4 8 16 32 64

    1 3 9 27 81 243 729

    1 4 16 64 256 1024 4096

    1 5 25 125 625 3125 15625

    1 6 6^2 6^3 6^4 6^5 6^6];

B=[1;3;2;1;3;2;1];

X = uptrbk(A,B)