
Accession Number : ADA115430
Title : AlternatingDirection 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 twodimensional selfadjoint 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 Anorm 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 AlternatingDirection 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