Something wrong with Matlab's LU decomposition:

Example:

A=[-1.0000 0.1667 -2.9897

0.3624 -1.0604 -0.5243

4.0990 -4.5547 7.0303]

[L,U]=lu(A)

L=[-0.2440 1.0000 0

0.0884 0.6964 1.0000

1.0000 0 0]

U=[4.0990 -4.5547 7.0303

0 -0.9445 -1.2746

0 0 -0.2583]

A correct answer is

L=[1.0000 0 0

-0.3624 1.0000 0

-4.0990 3.8714 1.0000]

U=[-1.0000 0.1667 -2.9897

0 -1.0000 -1.6078

0 0 1.0000]

[David Goodmanson]

Hi LK

There is nothing really wrong here. 'help lu' tells you that [L U] = lu(A) gives a row-permuted L matrix (it's not necessarily lower triangular any more) so that A = LU. The command [L U P] = lu(A) gives a true lower triangular matrix L and a permutation matrix P such that PA = LU, or (since P' is the inverse of P), A = P'LU. All of this done to allow pivoting so that the computed L and U have maximal numerical accuracy.