Solving Sparse Symmetric Sets of Linear Equations by Preconditioned Conjugate Gradients

An algorithm is described for solving sparse symmetric sets of linear equations whose matrix is positive defimte. An incomplete factonzation is formed and used to precondition the matrix for conjugate gradients and hence greatly reduce the number of iterations needed. The problem of choosing a reasonably accurate factorization without having too many fill-ms is considered. Results of a large number of test runs are presented. Code implementing the algorithm is described briefly.