LU Decomposition: Doolittle & Crout

Crout and Doolittle implmentations using vectorization.

LU decomposition or factorization represents the direct consequence of the following theorem:

Let . Then exists such that

For , we have:

Doolittle

This method considers . We have:

We can observe the following method in order to find the values of the L and U matrices:

1. We start with
2. For each , we compute
3. For each , we compute
4. For , we repeat the steps 2-3, but using the following formulas:

Crout

This method considers . We have:

We can observe the following method in order to find the values of the L and U matrices:

1. We start with
2. For each , we compute
3. For each , we compute
4. For , we repeat the steps 2-3, but using the following formulas:

References:

Metode numerice, Valeriu Iorga & Boris Jora, Editura Albastra Cluj-Napoca 2008.