Algebraic Analysis of Schwarz Methods for Singular Systems

  • Ivo Marek
  • Daniel B. Szyld
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 40)


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.


Singular System Domain Decomposition Method Stochastic Matrix Algebraic Formulation Nonnegative Matrice 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ivo Marek
    • 1
    • 2
  • Daniel B. Szyld
    • 1
    • 2
  1. 1.School of Civil EngineeringCzech Institute of TechnologyPrague
  2. 2.Department of MathematicsTemple UniversityUSA

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