1 2 011 115 SolutionA1 0 31 1 35 1 6 function L U P Q gecpA

Solution

A=[1 0 3;1 -1 -3;5 -1 6];
%function [L, U, P, Q] = gecp(A)
%GECP calculate Gauss elimination with complete pivoting
%
% (G)aussian (E)limination (C)omplete (P)ivoting
% Input : A nxn matrix
% Output
% L = Lower triangular matrix with ones as diagonals
% U = Upper triangular matrix
% P and Q permutations matrices so that P*A*Q = L*U
%
% See also LU
%
% written by : Cheilakos Nick
[n, n] = size(A);
p = 1:n;
q = 1:n;
for k = 1:n-1
[maxc, rowindices] = max( abs(A(k:n, k:n)) );
[maxm, colindex] = max(maxc);
row = rowindices(colindex)+k-1; col = colindex+k-1;
A( [k, row], : ) = A( [row, k], : );
A( :, [k, col] ) = A( :, [col, k] );
p( [k, row] ) = p( [row, k] ); q( [k, col] ) = q( [col, k] );
if A(k,k) == 0
break
end
A(k+1:n,k) = A(k+1:n,k)/A(k,k);
i = k+1:n;
A(i,i) = A(i,i) - A(i,k) * A(k,i);
end
L = tril(A,-1) + eye(n);
U = triu(A);
P = eye(n);
P = P(p,:);
Q = eye(n);
Q = Q(:,q);

L =   
  
1.00000 0.00000 0.00000
-0.50000 1.00000 0.00000
0.50000 -0.42857 1.00000

U =   
  
6.00000 5.00000 -1.00000
0.00000 3.50000 -1.50000
0.00000 0.00000 -0.14286

P =   
  
Permutation Matrix
  
0 0 1
0 1 0
1 0 0

Q =   
  
Permutation Matrix
  
0 1 0
0 0 1
1 0 0