منابع مشابه
Algebraic Schwarz Theory
This report contains a collection of notes on abstract additive and multiplicative Schwarz methods for self-adjoint positive linear operator equations. We examine closely one of the most elegant and useful modern convergence theories for these methods, following the recent work in the finite element multigrid and domain decomposition literature. Our motivation is to fully understand the structu...
متن کاملAn Algebraic Schwarz Theory
SCHWARZ THEORY 27 Algorithm 4.1 (Abstract Multiplicative Schwarz Method { Implementation Form) un+1 = MS(un; f) where the operation uNEW = MS(uOLD; f) is de ned as: Do k = 1; : : : ; J rk = IT k (f AuOLD) ek = Rkrk uNEW = uOLD + Ikek uOLD = uNEW End do. Note that the rst step through the loop in MS( ; ) gives: uNEW = uOLD + I1e1 = uOLD + I1R1IT 1 (f AuOLD) = (I I1R1IT 1 A)uOLD + I1R1IT 1 f: Con...
متن کاملAlgebraic theory of multiplicative Schwarz methods
1 Department ofMathematics andComputerScience,EmoryUniversity,Atlanta,GA30322, USA; e-mail: [email protected] 2 Fachbereich Mathematik, Universität Wuppertal, 42097 Wuppertal, Germany; e-mail: [email protected] 3 Fakultät für Mathematik, Universität Bielefeld, Postfach 10 01 31, 33501 Bielefeld, Germany; e-mail: [email protected] 4 Department of Mathematics, Te...
متن کاملAlgebraic Schwarz Methods for the Numerical Solution of Markov Chains
The convergence of additive and multiplicative Schwarz methods for computing certain characteristics of Markov chains such as stationary probability vectors and mean first passage matrices is studied. Our main result is a convergence theorem for multiplicative Schwarz iterations when applied to singular systems. As a by-product we also obtain a convergence result for alternating iterations. It ...
متن کاملAlgebraic Analysis of Schwarz Methods for Singular Systems
During the last few years, an algebraic formulation of Schwarz methods was developed. In this paper this algebraic formulation is used to prove new convergence results for multiplicative Schwarz methods when applied to consistent singular systems of linear equations. Coarse grid corrections are also studied. In particular, these results are applied to the numerical solutions of Markov chains.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Kyushu Journal of Mathematics
سال: 2011
ISSN: 1340-6116,1883-2032
DOI: 10.2206/kyushujm.65.299