If is a symmetric positive definite matrix, associated
linear equations are often solved using Choleski decomposition:

where is a lower triangular matrix. In practice this is followed by forward and back substitutions:

to complete the solution of . A pseudocode algorithm for Cholesky decomposition is

A parallel version, assuming the main array is stored by columns with the rows cyclically distributed, is given in figure 4.4. The array is accumulated in the lower part of the input array

Bryan Carpenter 2003-04-15