An original implementation in CMOS technology of the exponential function will be presented. In order to improve the circuit frequency response, only MOS transistors working in saturation are used and a current-mode operation is chosen. The compatibility to VLSI designed is achieved by using a FGMOS (Floating-Gate MOS) transistor for reducing the circuit complexity. The approximation error caus...

The purpose of this study is to construct a high-order interpolation and scheme for arbitrary scattered datasets. The resulting function approximation is an interpolation function when the dataset is exact, or a regression if measurement errors are present. We represent each datapoint with a Taylor series, and the approximation error as a combination of the derivatives of the the target functio...

In algorithms of nonlinear Kalman filter, the so-called extended Kalman filter algorithm actually uses first-order Taylor expansion approach to transform a nonlinear system into a linear system. It is obvious that this algorithm will bring some systematic deviations because of ignoring nonlinearity of the system. This paper presents two extended Kalman filter algorithms for nonlinear systems, c...

A series of hot-compression tests and Taylor-model simulations were carried out with the intention of developing a simple expression for the proof stress of magnesium alloy AZ31 during hot working. A crude approximation of wrought textures as a mixture of a single ideal texture component and a random background was employed. The shears carried by each deformation system were calculated using a ...

We introduce the concept of fast wavelet-Taylor Galerkin methods for the numerical solution of partial differential equations. In wavelet-Taylor Galerkin method discretization in time is performed before the wavelet based spatial approximation by introducing accurate generalizations of the standard Euler, and leap-frog time-stepping scheme with the help of Taylor series expansions in the time s...

We give a new method to construct minimal free resolutions of all monomial ideals. This relies on two concepts: one is the well-known lcm-lattice ideal; other concept called Taylor basis, which describes how resolution can be embedded in resolution. An approximation formula for ideals also obtained.

A treecode algorithm is presented for evaluating electrostatic potentials in a charged particle system undergoing screened Coulomb interactions in 3D. The method uses a farfield Taylor expansion in Cartesian coordinates to compute particle–cluster interactions. The Taylor coefficients are evaluated using new recurrence relations which permit efficient computation of high order approximations. T...

This technical report constructs a theoretical framework to relate standard Taylor approximation based optimisation methods with Natural Gradient (NG), a method which is Fisher efficient with probabilistic models. Such a framework will be shown to also provide mathematical justification to combine higher order methods with the method of NG.

We propose a novel interpretation of the collapsed variational Bayes inference with a zero-order Taylor expansion approximation, called CVB0 inference, for latent Dirichlet allocation (LDA). We clarify the properties of the CVB0 inference by using the αdivergence. We show that the CVB0 inference is composed of two different divergence projections: α = 1 and −1. This interpretation will help she...

David J. Nott, Siew Li Tan, Mattias Villani and Robert Kohn, Regression density estimation with variational methods and stochastic approximation, 2012, Journal of Computational And Graphical Statistics, (21), 3, 797-820. Journal of Computational And Graphical Statistics is available online at informaworld TM : http://dx.doi.org/10.1080/10618600.2012.679897 Copyright: American Statistical Associ...