Search results for "Taylor"
showing 10 items of 91 documents
The Taylor Rule and the Practice of Central Banking
2010
The Taylor rule has revolutionized the way many policymakers at central banks think about monetary policy. It has framed policy actions as a systematic response to incoming information about economic conditions, as opposed to a period-by-period optimization problem. It has emphasized the importance of adjusting policy rates more than one-for-one in response to an increase in inflation. And, various versions of the Taylor rule have been incorporated into macroeconomic models that are used at central banks to understand and forecast the economy. ; This paper examines how the Taylor rule is used as an input in monetary policy deliberations and decision-making at central banks. The paper charac…
On the integration of kinetic models using a high-order taylor series method
1992
A general equation to derive kinetic models up to any order is given. This equation greatly facilitates the application of the Taylor series method to the integration of kinetic models up to very high orders. When dealing with non-stiff models, computing time is always reduced by increasing the integration order, at least up to the 20th order. When the model is stiff, the integration order should be optimized; however, a twelfth order is recommended to integrate weakly stiff models. The use of an algorithm which permits the immediate calculation of the integration step size required to maintain a given accuracy leads to further reductions in computing time. When implemented as recommended h…
Comparison among three boundary element methods for torsion problems: CPM, CVBEM, LEM
2011
This paper provides solutions for De Saint-Venant torsion problem on a beam with arbitrary and uniform cross-section. In particular three methods framed into complex analysis have been considered: Complex Polynomial Method (CPM), Complex Variable Boundary Element Method (CVBEM) and Line Element-less Method (LEM), recently proposed. CPM involves the expansion of a complex potential in Taylor series, computing the unknown coefficients by means of collocation points on the boundary. CVBEM takes advantage of Cauchy’s integral formula that returns the solution of Laplace equation when mixed boundary conditions on both real and imaginary parts of the complex potential are known. LEM introduces th…
Method to find the Minimum 1D Linear Gradient Model for Seismic Tomography
2016
The changes in the state of a geophysical medium before a strong earthquake can be found by studying of 3D seismic velocity images constructed for consecutive time windows. A preliminary step is to see changes with time in a minimum 1D model. In this paper we develop a method that finds the parameters of the minimum linear gradient model by applying a two-dimensional Taylor series of the observed data for the seismic ray and by performing least-square minimization for all seismic rays. This allows us to obtain the mean value of the discrete observed variable, close to zero value.
Infrared-finite algorithms in QED II. The expansion of the groundstate of an atom interacting with the quantized radiation field
2009
Abstract In this paper, we present an explicit and constructive algorithm enabling us to calculate the groundstate and the groundstate energy of a non-relativistic atom minimally coupled to the quantized radiation field up to an error of arbitrary finite order in the fine structure constant. Because of infrared divergences, which invalidate a straightforward Taylor expansion, an iterative construction is employed to remove the infrared cut-off in photon momentum space and to produce a convergent algorithm.
Riesz fractional integrals and complex fractional moments for the probabilistic characterization of random variables
2012
Abstract The aim of this paper is the probabilistic representation of the probability density function (PDF) or the characteristic function (CF) in terms of fractional moments of complex order. It is shown that such complex moments are related to Riesz and complementary Riesz integrals at the origin. By invoking the inverse Mellin transform theorem, the PDF or the CF is exactly evaluated in integral form in terms of complex fractional moments. Discretization leads to the conclusion that with few fractional moments the whole PDF or CF may be restored. Application to the pathological case of an α -stable random variable is discussed in detail, showing the impressive capability to characterize…
Efficient formulation of Multimode Equivalent Networks for 2-D waveguide steps through Kummer's transformation
2017
In this paper we present a new and improved formulation for the Multimode Equivalent Network (MEN) representation of arbitrary waveguide junctions. In the new formulation the Kummer's transformation is used to separate the kernel into dynamic and static parts, by introducing higher order extraction terms. The main difference with respect to the old formulation is that the approximation of the kernel is more accurate and the numerical computations are more efficient. In addition to theory, both formulations are compared in terms of efficiency and convergence thereby fully validating the proposed new formulation.
Active controlled structural systems under delta-correlated random excitation: linear and nonlinear case
2006
Abstract Reduction of structural vibration in active controlled dynamical system is usually performed by means of convenient control forces dependent of the dynamic response. In this paper the existent studies will be extended to dynamical systems subjected to non-Gaussian random process accounting for the time delay involved in the application of active control actions. Control forces acting with time-delay effects will be expanded in Taylor series evaluating response statistics by means of the extended Ito differential rule to consider the effects of the non-normality of the input processes. Numerical application provided shows the feasibility of the proposed method to analyze stochastic …
Reprint of: Approximate Taylor methods for ODEs
2018
Abstract A new method for the numerical solution of ODEs is presented. This approach is based on an approximate formulation of the Taylor methods that has a much easier implementation than the original Taylor methods, since only the functions in the ODEs, and not their derivatives, are needed, just as in classical Runge–Kutta schemes. Compared to Runge–Kutta methods, the number of function evaluations to achieve a given order is higher, however with the present procedure it is much easier to produce arbitrary high-order schemes, which may be important in some applications. In many cases the new approach leads to an asymptotically lower computational cost when compared to the Taylor expansio…