Improving the efficiency of incomplete Choleski preconditionings

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Abstract
Techniques based on the idea of preconditioning have significantly improved the efficiency of classical iterative methods. In this work two preconditioning approaches based on incomplete Choleski factorization have been further refined, with the result that both storage requirements and solution times have been greatly improved. The first is based on the rejection of certain terms of the factorization process according to their magnitude. An efficient computational handling of the incomplete factorization is proposed which improves substantially the complicated addressings and the overall efficiency of the iterative method. The second preconditioning matrix is based on a rejection criterion relative to the position of the non‐zero terms of the coefficient matrix. Such preconditioners have been proposed in the past but experience with the application of the finite‐element method is not favourable since the factorization very often becomes unstable or the rate of convergence is not satisfactory. The modifications proposed here give this type of incomplete factorization both robustness and efficiency.

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