On the eigenvalues and eigenvectors of nonsymmetric saddle point matrices preconditioned by block triangular matrices

Block lower triangular and block upper triangular matrices are popular preconditioners for nonsymmetric saddle point matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned systems are related

Some observations on weighted GMRES

We investigate the convergence of the weighted GMRES method for solving linear systems. Two different weighting variants are compared with unweighted GMRES for three model problems, giving a phenomenological explanation of cases where weighting improves convergence, and a case where weighting has no effect on the convergence. We also present new alternative implementations of the weighted Arnoldi algorithm which may be favorable in terms of computational complexity, and examine stability issues connected with these implementations. Two implementations of weighted GMRES are compared for a large number of examples. We find that weighted GMRES may outperform unweighted GMRES for some problems, but more often this method is not competitive with other Krylov subspace methods like GMRES with deflated restarting or BICGSTAB, in particular when a preconditioner is used

Identification of Segments of Thermo Energy Plants with a Latent Class Model

This paper identifies different groups in a cost function framework of thermo energy plants belonging to EDP-Electricity of Portugal. In particular, we have clustered the sample - comprising data for years 1987 to 2006 - into two groups. To do so, we have implemented a stochastic frontier latent class model, a procedure that also permits us to analyze also the efficiency of the thermo energy plants with respect to their own frontiers. The results reveal that some of the plants could improve their efficiency levels substantially.cost efficiency; latent class model; thermo energy plants; stochastic frontier.

Geodesic excursions into cusps in finite-volume hyperbolic manifolds

18 pages, no figures.-- MSC1991 codes: Primary: 53C22; Secondary: 30F40, 58F17.MR#: MR1214056 (94d:53067)Zbl#: Zbl 0793.53052The main goal of the paper is to prove that, for a given non-compact hyperbolic $n$-manifold $M$ of finite volume, $p\in M$, and a number $\alpha$, $0\leq\alpha \leq 1$, the Hausdorff dimension of the set \{v\in T\sb p\sp 1(M): \lim\sb{t\to\infty} \sup (\text{dist} (\gamma\sb v(t),p)/t)\geq \alpha\} is equal to $n(1-\alpha)$, where \gamma\sb v(t) is the geodesic in $M$ emanating from $p$ in the direction of $v$. This generalize a result of [Acta Math. 149, 215-237 (1982)] that, for almost every direction $v$, such a limit is $1/n$, and it is one for just a countable set of directions $v$.\par However we remark that one has to restrict this claim to the class of hyperbolic manifolds with only Abelian parabolic cusps because the authors assume in fact such property for all considered manifolds $M$ [source: Zentralblatt MATH].Research supported by a grant from CICYT, Ministerio de Educación y Ciencia, Spain.Publicad

The Technical Efficiency of UK Airports

In this paper, the innovative random stochastic frontier model is used to estimate the technical efficiency of UK airports. These airports are ranked according to their total productivity for the period 2000-2005 and homogenous and heterogeneous variables in the cost function are disentangled, which leads us to advise the implementation of common policies as well as policies by segments. Economic implications arising from the study are also considered.Airports; UK; efficiency; random frontier models; policy implications.

The antitriangular factorisation of saddle point matrices

Mastronardi and Van Dooren recently introduced the block antitriangular ("Batman") decomposition for symmetric indefinite matrices. Here we show the simplification of this factorisation for saddle point matrices and demonstrate how it represents the common nullspace method. We show the relation of this factorisation to constraint preconditioning and how it transforms but preserves the block diagonal structure of block diagonal preconditioning

Natural preconditioners for saddle point systems

The solution of quadratic or locally quadratic extremum problems subject to linear(ized) constraints gives rise to linear systems in saddle point form. This is true whether in the continuous or discrete setting, so saddle point systems arising from discretization of partial differential equation problems such as those describing electromagnetic problems or incompressible flow lead to equations with this structure as does, for example, the widely used sequential quadratic programming approach to nonlinear optimization.\ud This article concerns iterative solution methods for these problems and in particular shows how the problem formulation leads to natural preconditioners which guarantee rapid convergence of the relevant iterative methods. These preconditioners are related to the original extremum problem and their effectiveness -- in terms of rapidity of convergence -- is established here via a proof of general bounds on the eigenvalues of the preconditioned saddle point matrix on which iteration convergence depends

Identification of Segments of Thermo Energy Plants with a Latent Class Model

This paper identifies different groups in a cost function framework of thermo energy plants belonging to EDP-Electricity of Portugal. In particular, we have clustered the sample - comprising data for years 1987 to 2006 - into two groups. To do so, we have implemented a stochastic frontier latent class model, a procedure that also permits us to analyze also the efficiency of the thermo energy plants with respect to their own frontiers. The results reveal that some of the plants could improve their efficiency levels substantially.cost efficiency; latent class model; thermo energy plants; stochastic frontier.