Incomplete Cholesky Preconditioners with Band-Diagonalization for Sparse Symmetric Systems

In this paper, we present a preconditioning method based on Incomplete Cholesky Decomposition (ICD) combined with a band-diagonalization strategy which enables an efficient ICD. The performance of the ICD preconditioner for sparse symmetric systems has a close relationship to the number of fill-ins of the exact Cholesky decomposition and the number can be decreased by the band-diagonalization. We consider an implicit surface reconstruction as a typical problem which has a property that the coefficient matrix can be transformed into a band-diagonal structure at a low computational cost. The effectiveness of the preconditioning is shown as a result of some numerical experiments. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)