This paper is concerned with the problem of computing approximate D-optimal design for polynomial regression with analytic weight function on a interval [m0-a, mo+ a]. It is shown that the structure of the optimal design depends on a and weight function. Moreover, the optimal support points and weights are analytic functions of a at a = 0. We make use of a Taylor expansion to provide a recursiv...

Polynomial interpolation to analytic functions can be very accurate, depending on the distribution of the interpolation nodes. However, in equispaced nodes and the like, besides being badly conditioned, these interpolants fail to converge even in exact arithmetic in some cases. Linear barycentric rational interpolation with the weights presented by Floater and Hormann can be viewed as blended p...

This paper presents a series expansion for the evolution of nonlinear systems which are analytic in the state and linear in the controls. An explicit recursive expression is obtained assuming that the input vector fields are constant. Additional simplifications take place in the analysis of systems described by second order polynomial vector fields. Sufficient conditions are derived to guarante...

Motivated by the recent work on symmetric analytic functions using concept of Faber polynomials, this article introduces and studies two new subclasses bi-close-to-convex quasi-close-to-convex associated with Janowski functions. By polynomial expansion method, it determines general coefficient bounds for belonging to these classes. It also finds initial coefficients bi-quasi-convex Some known c...

When investigating the dynamical properties of complex multiple-component physical and physiological systems, it is often the case that the measurable system's output does not directly represent the quantity we want to probe in order to understand the underlying mechanisms. Instead, the output signal is often a linear or nonlinear function of the quantity of interest. Here, we investigate how v...

In this paper, we propose a method for detecting patterns of interest in vector fields. Our method detects patterns in a scaleand rotation-invariant manner. It works by approximating the vector-field data locally using a Laurent polynomial weighted by radial basis functions. The proposed representation is able to model both analytic and non-analytic flow fields. Invariance to scale and rotation...