Cholesky Factorization

James Hembree Jr.

Cholesky’s factorization is an elegant theorem that allows us to efficiently factor a positive-definite, square matrix into a lower-triangular matrix multiplied by its complex conjugate. The eponymous result is due to the French military officer André-Louis Cholesky, and it was published posthumously after his untimely death during the tail end of World War I. My presentation seeks to explain background mathematics and background results, prove the theorem, and, using Python, demonstrate the efficiency of Cholesky’s factorization by comparing it with LU factorization.

• James Hembree graduated from Cold Springs Mennonite School in Abbeville. He is a transfer student who previously attended Piedmont Technical College. He is a graduating senior majoring in mathematics and minoring in philosophy. James is a peer tutor at Lander's Student Success Center, and he is heading to University of Tennessee, Knoxville to study for a PhD in mathematics this fall after graduating from Lander.