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MA61 Sparse symmetric positive-definite system: incomplete factorization

To solve a symmetric, sparse and positive definite set of linear equations Ax = b i.e.

j=1na ijxj = bi, i = 1,2,...,n.

The solution is found by a preconditioned conjugate gradient technique, where the preconditioning is done by incomplete factorization.

(a) MA61A performs the incomplete factorization based on an LDLT decomposition. New entries which have small numerical values compared to the corresponding diagonal entries are dropped, and the diagonal entries are modified to ensure positive definiteness. This results in a preconditioning matrix C held in LDLT form.
(b) MA61B performs the iteration procedure using the preconditioned coefficient matrix (i.e. AC1 ) as the iteration matrix for the conjugate gradient algorithm.