Efficient approximation of functions of some large matrices by partial fraction expansions

Some important applicative problems require the evaluation of functions $\Psi$ of large and sparse and/or \emph{localized} matrices $A$. Popular and interesting techniques for computing $\Psi(A)$ and $\Psi(A)\mathbf{v}$, where $\mathbf{v}$ is a vector, are based on partial fraction expansions. However, some of these techniques require solving several linear systems whose matrices differ from $A$ by a complex multiple of the identity matrix $I$ for computing $\Psi(A)\mathbf{v}$ or require inverting sequences of matrices with the same characteristics for computing $\Psi(A)$. Here we study the use and the convergence of a recent technique for generating sequences of incomplete factorizations of matrices in order to face with both these issues. The solution of the sequences of linear systems and approximate matrix inversions above can be computed efficiently provided that $A^{-1}$ shows certain decay properties. These strategies have good parallel potentialities. Our claims are confirmed by numerical tests

Patterns for service-oriented information exchange requirements

Service-Oriented Computing (SOC) is an emerging computing paradigm that supports loosely-coupled inter-enterprise interactions. SOC interactions are predominantly specified in a procedural manner that defines message sequences intermixing implementation with business requirements. In this paper we present a set of patterns concerning requirements of information exchange between participants engaging in service-oriented interactions. The patterns aim at explicating and elaborating the business requirements driving the interaction and separating them from implementation concerns

The Space of Geometric Limits of One-generator Closed Subgroups of PSL2(R)

We give a complete description of the closure of the space of one-generator closed subgroups of PSL2(R) for the Chabauty topology, by computing explicitly the matrices associated with elements of Aut(D) = PSL2(R), and finding quantities parametrizing the limit cases. Along the way, we investigate under what conditions sequences of maps transform convergent sequences of closed subsets of the domain into convergent sequences of closed subsets of the range. In particular, this allows us to compute certain geometric limits of PSL2(R) only by looking at the Hausdorff limit of some closed subsets of C.Comment: 28 pages, 6 figure

Optimal CDMA signatures: a finite-step approach

A description of optimal sequences for direct-sequence code division multiple access is a byproduct of recent characterizations of the sum capacity. The paper restates the sequence design problem as an inverse singular value problem and shows that it can be solved with finite-step algorithms from matrix analysis. Relevant algorithms are reviewed and a new one-sided construction is proposed that obtains the sequences directly instead of computing the Gram matrix of the optimal signatures

Multimodal and ubiquitous computing systems: supporting independent-living older users

We document the rationale and design of a multimodal interface to a pervasive/ubiquitous computing system that supports independent living by older people in their own homes. The Millennium Home system involves fitting a resident’s home with sensors – these sensors can be used to trigger sequences of interaction with the resident to warn them about dangerous events, or to check if they need external help. We draw lessons from the design process and conclude the paper with implications for the design of multimodal interfaces to ubiquitous systems developed for the elderly and in healthcare, as well as for more general ubiquitous computing applications