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:
a2 Scientific Computing and Computational Mathematics Program, Stanford University, Stanford, California 94305-9025, USA, E-mail:
a3 Institut für Mathematik, Technische Universität Berlin, D-10623 Berlin, Germany, E-mail:

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


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.

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


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.