Authors R. K. and J. M. would like to dedicate this paper to their former teacher of numerical mathematics Doc. RNDr. Jiří Kobza, CSc. on the occasion of his 70th birthday.
On the Moore–Penrose inverse in solving saddle-point systems with singular diagonal blocks†
Article first published online: 18 OCT 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Numerical Linear Algebra with Applications
Volume 19, Issue 4, pages 677–699, August 2012
How to Cite
Kučera, R., Kozubek, T., Markopoulos, A. and Machalová, J. (2012), On the Moore–Penrose inverse in solving saddle-point systems with singular diagonal blocks. Numer. Linear Algebra Appl., 19: 677–699. doi: 10.1002/nla.798
- Issue published online: 10 JUL 2012
- Article first published online: 18 OCT 2011
- Manuscript Accepted: 4 JUN 2011
- Manuscript Revised: 12 APR 2011
- Manuscript Received: 19 APR 2010
- Moore–Penrose inverse;
- orthogonal projectors;
- saddle-point systems;
- domain decomposition methods;
- condition number
This paper deals with the role of the generalized inverses in solving saddle-point systems arising naturally in the solution of many scientific and engineering problems when finite-element tearing and interconnecting based domain decomposition methods are used to the numerical solution. It was shown that the Moore–Penrose inverse may be obtained in this case at negligible cost by projecting an arbitrary generalized inverse using orthogonal projectors. Applying an eigenvalue analysis based on the Moore–Penrose inverse, we proved that for simple model problems, the number of conjugate gradient iterations required for the solution of associate dual systems does not depend on discretization norms. The theoretical results were confirmed by numerical experiments with linear elasticity problems. Copyright © 2011 John Wiley & Sons, Ltd.