On the wikipedia page of LU decomposition there is an algorithm that produce the decomposition. It is called Doolittle algorithm.
I'm really interested who is Doolittle? Or from where the name comes from? Is there any citation for the original work of the algorithm? As I know the decomposition is invented be Alan Turing.
A reference to the Doolittle's paper is missing on Wiki:
Doolittle, M.H.: Method employed in the solution of normal equations and the adjustment of a triangularization. In: U. S. Coast and Geodetic Survey, Report, pp. 115–120 (1878).
For more information, see Mathematicians of Gaussian Elimination by Grcar. Apparently, Doolittle worked as a computer.