Compensative Block Incomplete Factorizations (Revised)

摘要

The paper deals with the construction of block incomplete factorizations. A211u001eframework of compensative block incomplete factorization is introduced for 211u001esymmetric positive definite matrices. Matrix compensation is applied instead of 211u001eapproximate matrix inversion in factorization. Several ways to compute 211u001ecompensative inverses of matrices and matrix compensations for compensative block 211u001eincomplete factorizations are introduced. Emphasis is placed on Stieltjes 211u001ematrices. Upper bounds of the maximum eigenvalue of preconditioned matrices are 211u001eestimated when compensative block incomplete factorization is applied to an 211u001eelliptic equation. Under a certain condition, upper bounds for all eigenvalues 211u001eare also estimated. With diagonally compensative inversion, parallel compensative 211u001eblock incomplete factorization is also presented. Numerical experiments show that 211u001ecompensative block incomplete factorization is an efficient and reliable 211u001epreconditioning technique.