2. Cholesky Factorization We would like to compute the solution to a system of linear equations
AX = B, where A is real symmetric or complex Hermitian and, in either
case, positive definite matrix, X and B are rectangular matrices or vectors.
The Cholesky decomposition can be used to factor A, A = LL T or A = U T U, where U is an upper triangular matrix and L is a lower triangular (L = U T ). The factored form of A is then used to solve the system of equations
AX = B. A recursive algorithm of Cholesky factorization is described in detail in
[18, 8]. Here we give the final recursive algorithms for the lower triangular
and upper triangular cases. We assume that A is n by n.
