In this paper we present a new approach towards global passive approximation in order to find a passive real-rational transfer function G(s) that is an arbitrarily close approximation of the passive transfer function nearest to a non-passive square transfer function H(s). It is based on existing solutions to pertinent matrix nearness problems. It is shown that the key point in constructing the ...

&bstract. The notions of a situation and a distance between situations in a narrow subject domain are introduced. ~ approach to the construction of an intellectual data base is suggested. The main task.of this data base is to find situations ~lhich are near to the one fixed by user. The theory of finite groups is considered as an example° I INTRODUCTION No~ information retrieval systems and esp...

We first prove the equivalence between some conditions of nearness and accretivity for nonlinear operators. Then we show an easier proof of a result of Tarsia regarding the equivalence of Cordes and Campanato conditions. 2000 Mathematics Subject Classification: 35H20, 46B20, 47H06.

This paper introduces the paradigm of optimization under uncertainty for modelling and solving matrix nearness problems. In particular, it considers the concrete problem of recovering correlation matrices from uncertain observations by introducing two different approaches to tackling uncertainty. The first approach invokes the framework of robust optimization to construct low error solutions th...

thought allows us to transcend the particularities of our specific place. This ability allows us to look past our own species and enter into relationships with other animals that amount to more than simply seeing them as objects for our consumption. On the other hand, our closest biological relatives, the Neanderthals, failed to form relationships with other animals that approach anywhere near ...

We discuss three types of sparse matrix nearness problems: given a sparse symmetric matrix, find the matrix with the same sparsity pattern that is closest to it in Frobenius norm and (1) is positive semidefinite, (2) has a positive semidefinite completion, or (3) has a Euclidean distance matrix completion. Several proximal splitting and decomposition algorithms for these problems are presented ...

Apartness spaces were introduced as a constructive counterpart to proximity spaces which, in turn, aimed to model the concept of nearness of sets in a metric or topological environment. In this paper we introduce apartness algebras and apartness frames intended to be abstract counterparts to the apartness spaces of Bridges and Vîta [3], and we prove a discrete duality for them.