Let P be a convex polytope in the d-dimensional Euclidean space. We consider an interpolation of a function f at the vertices of P and compare it with the interpolation of f and its derivative at a fixed point y ∈ P. The two methods may be seen as multivariate analogues of an interpolation by secants and tangents, respectively. For twice continuously differentiable functions, we establish sharp...

Talbot’s method for the numerical inversion of the Laplace transform consists of numerically integrating the Bromwich integral on a special contour by means of the trapezoidal or midpoint rules. In this paper we address the issue of parameter selection in the method, for the particular situation when parabolic PDEs are solved. In the process the well-known subgeometric convergence rate O(exp(−c...

The paper deals with the trapezoidal rule discretization of a class of linear delay differential equations, with a special emphasis on equations with a proportional delay. Our purpose is to analyse the asymptotic properties of the numerical solutions and formulate their upper bounds. We also survey the known results and show that our formulae improve and generalize these results. In particular,...

In this paper, we introduce a method to obtain the nearest trapezoidal approximation of fuzzy numbers so that preserving conditions expect interval and include the core of a fuzzy number.

We introduce a tractable multi-issue model of electoral competition in which candidates are exogenously committed to particular positions on a subset of issues, while they can choose a sequence of binary positions for the remaining issues to maximize their winning probability. A majorityefficient position is defined as one where a candidate cannot make a majority of the electorate better off, t...

Sources providing information about the value of a variable may not be totally reliable. In such a case, it is common in uncertainty theories to take account of this unreliability by a so-called discounting rule. A few discounting rules have been proposed in the framework of imprecise probability theory, but one of the drawback of those rules is that they do not preserve interesting properties ...

The problem to find the nearest trapezoidal approximation of a fuzzy number with respect to a well-knownmetric, which preserves the expected interval of the fuzzy number, is completely solved. The previously proposed approximation operators are improved so as to always obtain a trapezoidal fuzzy number. Properties of this new trapezoidal approximation operator are studied. © 2007 Elsevier B.V. ...

In this contribution we present an application of metric rule generation in the domain of medical research. We consider intensive care unit patients developing a septic shock during their stay at the hospital. To analyse the patient data, rule generation is embedded in a medical data mining cycle. For rule generation, we improve an architecture based on a growing trapezoidal basis function netw...

Backward induction is the most widely accepted principle for predicting behavior in dynamic games. In experiments, however, players frequently violate this principle. An alternative is a 2-parameter “dynamic level-k” model, where players choose a rule from a rule hierarchy. The rule hierarchy is iteratively defined such that the level-k rule is a best-response to the level-(k − 1) rule and the ...