Chapter 2

Efficient Preconditioners for Saddle Point Systems

Zhi-Hao Cao

Abstract

<p>Various block preconditioners for two by two block linear saddle point systems are studied. All block preconditioners are derived from a splitting of the (1,1) block of the two by two block matrix. We analyze the properties of the corresponding preconditioned matrices, in particular their spectra, and discuss the computational performance of the preconditioned iterative methods. It is shown that fast convergence depends mainly on the quality of the splitting of the (1,1) block. Moreover, some strategies of the implementation of the block preconditioners based on purely algebraic considerations are discussed. Thus, applying our block preconditioners to the related saddle point problems, we obtain preconditioned iterative methods in a “black box” fashion.</p>

Total Pages: 23-43 (21)

Purchase Chapter  Book Details

RELATED BOOKS

.The Generalized Relative Gol’dberg Order and Type: Some Remarks on Functions of Complex Variables.
.Subharmonic Functions, Generalizations, Holomorphic Functions, Meromorphic Functions, and Properties.
.Predictive Analytics Using Statistics and Big Data: Concepts and Modeling.
.Differential and Integral Calculus - Theory and Cases.