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Math Help - Upper triangularization method (AX=B)

  1. #1
    Newbie
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    Oct 2009
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    Upper triangularization method (AX=B)

    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

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




    The above program is to construct the solution to AX=B by reducing the augmented matrix [A B] to upper triangularization method and then performing back substitution.

    I am trying to modify this program so that it will solve M linear systems with the same coefficient matrix A but different column matrices B . The M linear systems look like AX1 = B1 AX2 = B2 ...... AXm=Bm
    (1 , 2 and m are in subscript)


    Please help!!!
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  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
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    someplace
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    4
    Quote Originally Posted by shobii View Post
    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

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




    The above program is to construct the solution to AX=B by reducing the augmented matrix [A B] to upper triangularization method and then performing back substitution.

    I am trying to modify this program so that it will solve M linear systems with the same coefficient matrix A but different column matrices B . The M linear systems look like AX1 = B1 AX2 = B2 ...... AXm=Bm
    (1 , 2 and m are in subscript)


    Please help!!!
    My guess is it should work as it is, just make B the matrix of the column vectors, all right you will have to modify the back substitution to do back sub for all the columns of augmentation (this can be done by looping over the extra columns, though the back substitution function might just work if you give it all the augmentation cols at once).

    CB
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