An O(N(logN)2/ loglogN) algorithm for computing the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast transform for converting between Legendre and Chebyshev coefficients with a Taylor series expansion for Chebyshev polynomials about equallyspaced points in the frequency domain. Both components are based on the FFT, and as an intermediate...

----------------------------------------------------------------------------------------------------------------This paper presents an algorithm that computes Taylor series expansions of order k=2, 3, 4 of the policy function of non-linear rational expectations models. Approximations of order 2 k ≥ may be markedly more accurate than linear approximations (k=1) if the variability of the exogenou...

We use generalized Taylor formulae in order to give some simple constructions in the real closure of an ordered valued field. We deduce a new, simple quantifier elimination algorithm for real closed valued fields and some theorems about constructible subsets of real valuative affine space.

We introduce a new method to approximate algebraic space curves. The algorithm combines a subdivision technique with local approximation of piecewise regular algebraic curve segments. The local technique computes pairs of polynomials with modified Taylor expansions and generates approximating circular arcs. We analyze the connection between the generated approximating arcs and the osculating ci...

In this article, we justify the use of parametric planar Pythagorean Hodograph spline curves in path planning. The elegant properties of such splines enable us to design an efficient interpolator algorithm, more precise than the classical Taylor interpolators and faster than an interpolator based on arc length computations.

The unconstrained minimization of a sufficiently smooth objective function f(x) is considered, for which derivatives up to order p, p ≥ 2, are assumed to be available. An adaptive regularization algorithm is proposed that uses Taylor models of the objective of order p and that is guaranteed to find a firstand second-order critical point in at most O (

In this paper we present a new model-based compensation technique called Delta Vector Taylor Series (DVTS). This new technique is an extension and improvement over the Vector Taylor Series (VTS) approach [7] that addresses several of its limitations. In particular, we present a new statistical representation for the distribution of clean speech feature vectors based on a weighted vector codeboo...

In this paper we consider the problem of chore division, which is closely related to a classical question, due to Steinhaus [7], of how to cut a cake fairly. We focus on constructive solutions, i.e., those obtained via a well-defined procedure or algorithm. Among the many notions of fairness is envy-freeness: an envy-free cake division is a set of cuts and an allocation of the pieces that gives...

We present state-of-the-art numerical simulations of a two-dimensional Rayleigh-Taylor instability for a compressible stratified fluid. We describe the computational algorithm and its implementation on the QPACE supercomputer. High resolution enables the statistical properties of the evolving interface that we characterize in terms of its fractal dimension to be studied.

Enter Uncertainty Representation Traditional Approach Traditional Approach: . . . Main Idea Taylor Model-Type . . . Technical Details Example of Using LP Example: Intervals . . . New Approach Other Examples General Comment . . . Traditional Trust & Its . . . Probabilistic . . . Possibly Dependent . . . Precise Formulation of . . . This Problem Is . . . Possibly Dependent . . . Acknowledgments A...