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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,… (More)

- Eric de Sturler, Jörg Liesen
- SIAM J. Scientific Computing
- 2005

We study block-diagonal preconditioners and an efficient variant of constraint preconditioners for general two-by-two block linear systems with zero (2,2)-block. We derive block-diagonal… (More)

- Jörg Liesen, Petr Tichý
- 2005

One of the most powerful tools for solving large and sparse systems of linear algebraic equations is a class of iterative methods called Krylov subspace methods. Their sign ficant advantages like low… (More)

- Jörg Liesen, Beresford N. Parlett
- Numerische Mathematik
- 2008

Linear systems in saddle point form are often symmetric and highly indefinite. Indefiniteness, however, is a major challenge for iterative solvers such as Krylov subspace methods. It has been noted… (More)

- Jörg Liesen, Zdenek Strakos
- SIAM J. Matrix Analysis Applications
- 2004

Abstract. We analyze the residuals of GMRES [9], when the method is applied to tridiagonal Toeplitz matrices. We first derive formulas for the residuals as well as their norms when GMRES is applied… (More)

- Jörg Liesen, Miroslav Rozlozník, Zdenek Strakos
- SIAM J. Scientific Computing
- 2002

We study Krylov subspace methods for solving unsymmetric linear algebraic systems that minimize the norm of the residual at each step (minimal residual (MR) methods). MR methods are often formulated… (More)

- Jörg Liesen, Zdenek Strakos
- SIAM J. Scientific Computing
- 2005

When GMRES [Y. Saad and M. H. Schultz, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856–869] is applied to streamline upwind Petrov–Galerkin (SUPG) discretized convectiondiffusion problems, it… (More)

- Jörg Liesen, Zdenek Strakos
- SIAM Review
- 2008

We analyze necessary and sufficient conditions on a nonsingular matrix A such that, for any initial vector r0, an orthogonal basis of the Krylov subspaces Kn(A, r0) is generated by a short… (More)

- Jörg Liesen, Paul E. Saylor
- SIAM J. Numerical Analysis
- 2005

We study necessary and sufficient conditions that a nonsingular matrix A can be B-orthogonally reduced to upper Hessenberg form with small bandwidth. By this we mean the existence of a decomposition… (More)

- Jörg Liesen
- SIAM J. Matrix Analysis Applications
- 2007

We show that the adjoint A+ of a matrix A with respect to a given inner product is a rational function in A, if and only if A is normal with respect to the inner product. We consider such matrices… (More)