Alternating-Direction Incomplete Factorizations.
Abstract
To solve the system of linear equations Aw = r that arises from the discretization of a two-dimensional self-adjoint elliptic differential equation, iterative methods employing easily computed incomplete factorization, LU = A+B, are frequently used. Dupont, Kendall, and Rachford showed that, for the DKR factorization, the number of iterations (arithmetic operations) required to reduce the A-norm of the error by a factor of epsilon is O(h to the minus 1/2 power log 1 epsilon) (O(h to the minus 2 and 1/2 power log 1 epsilon)), where h is the stepsize used in the discretization. We present some error estimates which suggest that, if a pair of Alternating-Direction DKR Factorizations are used, then the number of iterations (arithmetic operations) may be decreased to O(h to the minus 1/3 power log 1 epsilon) (O(h to the minus 2 and 1/3 power log 1 epsilon)). Numerical results supporting this estimate are included. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 19, 1981
- Accession Number
- ADA115430
Entities
People
- Benren Zhu
- Kenneth R. Jackson
- Tony F. Chan
Organizations
- Yale University