Paper Info
Title
Some Computational Results on “Two-Line” Iterative Methods for the Biharmonic Difference Equation
Abstract
"Two-line" iterative schemes for the biharmonic difference equation have been discussed in several recent works. This approach was first suggested by J. Heller [2] who noticed that such schemes are "three-block schemes" and hence many advantages are realized. Motivated by Heller's remarks, Varga [5] and the present author [3] independently developed useful methods of solving two-line equations. In that earlier work we also obtained estimates from above on ),a, hE, and hE, the spectral radii of the iteration matrices for the Richardson (simultaneous displacement), Liebmann (successive displacement), and Extrapolated Liebmann (over-relaxation, successive displacement) schemes respectively. More recently [4] we have also obtained estimates from below for these quantities. The purpose of this note is to report on some results of actual calculational experiments which we performed to obtain the true values of these eigenvalues in several cases. These results are then compared with the previously given estimates. In section 2 we discuss the general problem and present a discussion of the problem and earlier results. Our specific calculations together with the results are described in section 3. These calculations were all performed on the IBM 650 of the Research Computing Center, Indiana University. We are indebted to Mrs. Margaret Olsen and Miss Barbara Rose who programmed these calculations.
Year
DOI
Venue
1961
10.1145/321075.321079
Journal of the ACM (JACM)
Keywords
DocType
Volume
Iterative Methods,Computational Results,Biharmonic Difference Equation
Journal
8
Issue
ISSN
Citations 
3
0004-5411
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Seymour V. Parter1207.48