Title:     Lower bounds for three-dimensional nonoverlapping domain 
           decomposition algorithms

Authors:   Susanne C. Brenner and Qingmi He

Published: Numerische Mathematik
           v. 93 (2003), 445-470
           online publication: January 30, 2002
           DOI 10.1007/s002110100376 

Abstract:  Lower bounds for the condition numbers of the preconditioned 
           systems are obtained for the wire basket preconditioner and 
           the Neumann-Neumann preconditioner in three dimensions. They 
           show that the known upper bounds are sharp.




 
paper:Numerische Mathematik