Solving a large, sparse, symmetric linear system Ax = b iteratively must use appropriate methods. The conjugate gradient (CG) method can break down if A is indefinite while algorithms such as SYMMLQ and MINRES, though stable for indefinite systems, are computationally more expensive than CG when applied to positive definite matrices. In this paper, we present an iterative method for the case wh...

We prove several residual bounds for relative perturbations of the eigenvalues of indefinite Hermitian matrix. The bounds fall into two categories – the Weyl-type bounds and the Hofmann–Wielandt-type bounds. The bounds are expressed in terms of sines of acute principal angles between certain subspaces associated with the indefinite decomposition of the given matrix. The bounds are never worse t...

Unlike Germanic, Italian and many other languages from different language families allow whclauses to occur as the complement of existential predicates and be interpreted as indefinites. I call these whclauses indefinite free relatives. A compositional semantics will be given for indefinite free relatives that is based on Jacobson’s (1995) proposal for the semantics of whwords. In a nutshell, I...

The aim of this paper is to show that Uzbek has the crosslinguistically rather unusual property of using two indefinite articles, namely the expressions bir and bitta. From a synchronic perspective the two indefinite articles can be shown to compete (at least in certain environments), and from a diachronic perspective there is evidence that bitta significantly expands to the expense of bir. The...

We consider a stochastic linear–quadratic (LQ) problem with possible indefinite cost weighting matrices for the state and the control. An outstanding open problem is to identify an appropriate Riccati-type equation whose solvability is equivalent to the solvability of this possibly indefinite LQ problem. In this paper we introduce a new type of differential Riccati equation, called the generali...

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.

The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exi...

This work offers experimental support for the hypothesis that some indefinite noun phrases do not only introduce new referents but also equip them with a certain ‘forward-looking potential’ which informs the hearer about the ‘importance’ of the referent in the subsequent discourse. Developing means to empirically account for the intuitions that exist with respect to English this-indefinites, I ...