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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 a. Note that the array m has a replicated distribution, so the
remap operation is a broadcast of the relevant part of column