Accession Number : ADA115430

Title :   Alternating-Direction Incomplete Factorizations.

Descriptive Note : Technical rept.,

Corporate Author : YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE

Personal Author(s) : Chan,Tony F ; Jackson,Kenneth R ; Zhu,Benren

PDF Url : ADA115430

Report Date : 19 Aug 1981

Pagination or Media Count : 48

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)

Descriptors :   *Linear algebraic equations, *Factor analysis, Iterations, Errors, Estimates, Arithmetic, Operation, Normal distribution, Ellipses, Numerical analysis

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE