We say that a symmetric matrix K is quasi-definite if it has the form K = [ −E AT A F ] where E and F are symmetric positive definite matrices. Although such matrices are indefinite, we show that any symmetric permutation of a quasi-definite matrix yields a factorization LDLT . We apply this result to obtain a new approach for solving the symmetric indefinite systems arising in interior-point m...

Natural languages possess a wealth of indefinite forms that typically differ in distribution and interpretation. Although formal semanticists have strived to develop precise meaning representations for different indefinite functions, to date there has hardly been any corpus work on the topic. In this paper, we present the results of a small corpus study where English indefinite forms any and so...

A new class of preconditioners is proposed for the iterative solution of symmetric indefinite systems arising from interior-point methods. The use of logarithmic barriers in interior point methods causes unavoidable ill-conditioning of linear systems and, hence, iterative methods fail to provide sufficient accuracy unless appropriately preconditioned. Now we introduce two types of preconditione...

This paper considers a multigrid algorithm suitable for efficient solution of indefinite linear systems arising from finite element discretization of time harmonic Maxwell equations. In particular, a “backslash” multigrid cycle is proven to converge at rates independent of refinement level if certain indefinite block smoothers are used. The method of analysis involves comparing the multigrid er...

Indefinite noun phrases introduce new discourse referents equipped with different referential and discourse properties. Indefinites can show wide or narrow scope behavior and they can be interpreted as specific or non-specific. Indefinites also show different discourse effects such as different degrees of discourse prominence. In this paper we present the results of two psycholinguistic pilot s...

The recent introduction of indefinite SVM by Luss and d’Aspremont [15] has effectively demonstrated SVM classification with a non-positive semi-definite kernel (indefinite kernel). This paper studies the properties of the objective function introduced there. In particular, we show that the objective function is continuously differentiable and its gradient can be explicitly computed. Indeed, we ...

This paper presents an approach to integrate the concepts of indefinite information with certainty factor in an object-oriented framework. In this work, the concept of traditional indefinite information is extended to include certainty factors so that indefiniteness can be measured. Indefinite information with certainty factors is classified into two categories: certainty factors of association...

we obtain the expression of ricci tensor for a $gcr$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $gcr$-lightlike submanifold of anindefinite complex space form. moreover, we have proved that everyproper totally umbilical $gcr$-lightlike submanifold of anindefinite kaehler manifold is a totally geodesic $gcr$-lightlikesubmanifold.

A selfadjoint involutive matrix J endows Cn with an indefinite inner product [·, ·] given by [x,y] = 〈Jx,y〉 , x,y ∈ Cn. Characterizations of the J -chaotic order Log(A) J Log(B) are presented for J -selfadjoint matrices A,B with positive eigenvalues, in terms of operator functions involving the α -power mean and the J -relative entropy. An indefinite complete form of the Furuta inequality and s...

In a metric g.f.f -manifold we study lightlike hypersurfaces M tangent to the characteristic vector fields, and owing to the presence of the f -structure, we determine some decompositions of TM and of a chosen screen distribution obtaining two distributions invariant with respect to the structure. We discuss the existence of a g.f.f -structure on a lightlike hypersurface and, under suitable hyp...