Acta Numerica



Numerical solution of saddle point problems


Michele Benzi a1 1 , Gene H. Golub a2 2 and Jörg Liesen a3 3
a1 Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322, USA, E-mail: benzi@mathcs.emory.edu
a2 Scientific Computing and Computational Mathematics Program, Stanford University, Stanford, California 94305-9025, USA, E-mail: golub@sccm.stanford.edu
a3 Institut für Mathematik, Technische Universität Berlin, D-10623 Berlin, Germany, E-mail: liesen@math.tu-berlin.de

Article author query
benzi m   [Google Scholar] 
golub gh   [Google Scholar] 
liesen j   [Google Scholar] 
 

Abstract

Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.


Dedication:
We dedicate this paper to Gil Strang on the occasion of his 70th birthday


Footnotes

1 Supported in part by the National Science Foundation grant DMS-0207599.

2 Supported in part by the Department of Energy of the United States Government.

3 Supported in part by the Emmy Noether Programm of the Deutsche Forschungs-gemeinschaft.