LU factorization

Question

Basically what I need to do is this:

Write an algorithm that finds the LU factorization of the following matrix. The algorithm should perform the necessary elementary row operations to reduce A to U, and store the various multipliers in each step. The output of the program should be two matrices: L and U.

A={{3,1,2}{6,3,4},{3,1,5}}

I can't use any of the built in code for LU or partial pivoting or any of that stuff that will finish it off with one function. I just need a little help getting started being as how I'm still new to programming. I know how I would do it all manually but writing the code for a general algorithm is eluding me. I'll obviously need to use for loops to test if

A[[2,1]]=0, A[[3,1]]=0

And that is about as far as I am. Any help would be greatly appreciated.

In any case, you'll want to look up Golub and Van Loan; there's a nice discussion there on how to implement this. — J. M.'s missing motivation, Oct 30 '15 at 03:22
Problems with your matrix? Check using PseudoInverse[{{3, 1, 2} {6, 3, 4}, {3, 1, 5}}] — thils, Oct 30 '15 at 07:03
@thils, for somebody just starting to understand Gaussian elimination, SVD is like handing a toddler a mountain bike. — J. M.'s missing motivation, Oct 30 '15 at 08:16
@JM What I am trying to convey is that LU factorization will run into problems for matrices with no inverse or near singular matrices. — thils, Oct 30 '15 at 09:05
@thils, yes, but that's something usually discussed after a full understanding of GE. Baby steps, and all that. — J. M.'s missing motivation, Oct 30 '15 at 10:18
Must you write the code? I ask because: (i) Mathematica already has a built-in function LUDecomposition; and (ii) such code is already out there on the web, and a search will lead you to it (forget that if this is a homework assignment!). — murray, Oct 30 '15 at 17:11
@murray The matrix must be non-singular for built-in function to work. — thils, Oct 30 '15 at 20:24

LU factorization

0 Answers0