Part I [13] introduces the application of the barycentric approximation methodology for evaluating pro t-and-loss distributions numerically. Although, convergence of the quantiles is ensured by the weak convergence of the discrete measures, as proclaimed in [13], recent numerical results have indicated that the approximations of the pro t-and-loss distribution are less practical when the portfo...

Given a convex polytope P , a set of coordinate functions attached to the vertices of P is barycentric if the functions are non-negative on P and reproduce linear functions sampled at the vertices of P . Warren (1996) describes a construction for rational barycentric coordinate functions of degree n d where d is the dimension of P and n is the number of facets of P . In this paper, we show that...

It is proved that the critical cells of a discrete Morse function in the sense of Forman on a finite regular CW complex can always be detected by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the barycentric subdivision of the complex. The proof is stated in terms of discrete Morse functions on a class of posets that is slightly broader t...

We investigate the barycentric associativity property for functions with indefinite arities and discuss the more general property of barycentric preassociativity, a generalization of barycentric associativity which does not involve any composition of functions. We also provide a generalization of Kolmogoroff-Nagumo’s characterization of the quasi-arithmetic mean functions to barycentrically pre...

Derivatives of polynomial interpolants lead in a natural way to approximations of derivatives of the interpolated function, e.g., through finite differences. We extend a study of the approximation of derivatives of linear barycentric rational interpolants and present improved finite difference formulas arising from these interpolants. The formulas contain the classical finite differences as a s...

In this article we describe the notion of affinely indepedent subset of a real linear space. First we prove selected theorems concerning operations on linear combinations. Then we introduce affine indepedence and prove the equivalence of various definitions of this notion. We also introduce the notion of the affine hull, i.e. a subset generated by a set of vectors which is an intersection of al...

We propose a simple generalization of Shephard’s interpolation to piecewise smooth, convex closed curves that yields a family of boundary interpolants with linear precision. Two instances of this family reduce to previously known interpolants: one based on a generalization of Wachspress coordinates to smooth curves and the other an integral version of mean value coordinates for smooth curves. A...

We construct representations of the Cuntz algebra O3 from real cubic transformations on closed intervals. By intertwining relations of transformations, we have those of operators of representations of O2 and O3. By these relations, we show that such representations are unitarily equivalent to barycentric representations.

We expose a relationship between jamming and a generalization of Tutte’s barycentric embedding. This provides a basis for the systematic treatment of jamming and maximal packing problems on two-dimensional surfaces.

Most of the existing dextrous robot hand preshape schemes offer grasp choice from a fmite and discrete set of grasp types. Such a discrete set obviously hinders the applicability of pre shaping schemes to complex and versatile task requirements. In this paper, we formulate the continuous spaces of grasps and derive an algo­ rithmic procedure for robot hand preshaping. The proposed procedure con...