Search results for "Gaussia"
showing 10 items of 653 documents
Approximation Operators of Binomial Type
1999
Our objective is to present a unified theory of the approximation operators of binomial type by exploiting the main technique of the so- called “ umbral calculus” or “finite operator calculus” (see [18], [20]-[22]). Let us consider the basic sequence (bn)n≥0 associated to a certain delta operator Q. By supposing that b n (x) ≥ 0, x ∈ [0, ∞), our purpose is to put in evidence some approximation properties of the linear positive operators (L Q n ) n≥1 which are defined on C[0,1] by \( L_n^Qf = \sum\limits_{k = 0}^n {\beta _n^Q{,_k}f\left( {\frac{k}{n}} \right),\beta _{n{,_k}}^Q\left( x \right): = } \frac{1}{{{b_n}\left( n \right)}}\left( {\begin{array}{*{20}{c}} n \\ k \end{array}} \right){b_…
Error Bounds for the Numerical Evaluation of Integrals with Weights
1988
This paper is concerned with a procedure of obtaining error bounds for numerically evaluated integrals with weights. If \( - \infty \mathop < \limits_ = a < b\mathop < \limits_ = \infty \), w integrable over [a,b] and positive almost everywhere, then an approximation of \({I_W}f: = \int\limits_a^b {w\left( t \right)f\left( t \right)dt} \) by a quadrature rule \({Q_n}f: = \sum\limits_{i = 0}^n {{\alpha _i}f\left( {{t_i}} \right)} \) is leading to the error Enf ≔ Iwf ‒ Qnf. An algorithm is derived for the computation of bounds for |Enf| depending on the smoothness of the integrand f and on the degree of exactness of Q. As initial values this algorithm needs moments of the weighting function w…
An analysis of Ralston's quadrature
1987
Ralston's quadrature achieves higher accuracy in composite rules than analogous Newton-Cotes or Gaussian formulas. His rules are analyzed, computable expressions for the weights and knots are given, and a more suitable form of the remainder is derived.
Population Monte Carlo Schemes with Reduced Path Degeneracy
2017
Population Monte Carlo (PMC) algorithms are versatile adaptive tools for approximating moments of complicated distributions. A common problem of PMC algorithms is the so-called path degeneracy; the diversity in the adaptation is endangered due to the resampling step. In this paper we focus on novel population Monte Carlo schemes that present enhanced diversity, compared to the standard approach, while keeping the same implementation structure (sample generation, weighting and resampling). The new schemes combine different weighting and resampling strategies to reduce the path degeneracy and achieve a higher performance at the cost of additional low computational complexity cost. Computer si…
GAMIT - A Fading-Gaussian Activation Model of Interval-Timing: Unifying Prospective and Retrospective Time Estimation
2014
Two recent findings constitute a serious challenge for all existing models of interval timing. First, Hass and Hermann (2012) have shown that only variance-based processes will lead to the scalar growth of error that is characteristic of human time judgments. Secondly, a major meta-review of over one hundred studies of participants’ judgments of interval duration (Block et al., 2010) reveals a striking interaction between the way in which temporal judgments are queried (i.e., retrospectively or prospectively) and cognitive load. For retrospective time judgments, estimates under high cognitive load are longer than under low cognitive load. For prospective judgments, the reverse pattern holds…
A Random Trajectory Approach for the Development of Nonstationary Channel Models Capturing Different Scales of Fading
2017
This paper introduces a new approach to developing stochastic nonstationary channel models, the randomness of which originates from a random trajectory of the mobile station (MS) rather than from the scattering area. The new approach is employed by utilizing a random trajectory model based on the primitives of Brownian fields (BFs), whereas the position of scatterers can be generated from an arbitrarily 2-D distribution function. The employed trajectory model generates random paths along which the MS travels from a given starting point to a fixed predefined destination point. To capture the path loss, the gain of each multipath component is modeled by a negative power law applied to the tra…
SVM approximation for real-time image segmentation by using an improved hyperrectangles-based method
2003
A real-time implementation of an approximation of the support vector machine (SVM) decision rule is proposed. This method is based on an improvement of a supervised classification method using hyperrectangles, which is useful for real-time image segmentation. The final decision combines the accuracy of the SVM learning algorithm and the speed of a hyperrectangles-based method. We review the principles of the classification methods and we evaluate the hardware implementation cost of each method. We present the combination algorithm, which consists of rejecting ambiguities in the learning set using SVM decision, before using the learning step of the hyperrectangles-based method. We present re…
Highlighting numerical insights of an efficient SPH method
2018
Abstract In this paper we focus on two sources of enhancement in accuracy and computational demanding in approximating a function and its derivatives by means of the Smoothed Particle Hydrodynamics method. The approximating power of the standard method is perceived to be poor and improvements can be gained making use of the Taylor series expansion of the kernel approximation of the function and its derivatives. The modified formulation is appealing providing more accurate results of the function and its derivatives simultaneously without changing the kernel function adopted in the computation. The request for greater accuracy needs kernel function derivatives with order up to the desidered …
Ownership protection of plenoptic images by robust and reversible watermarking
2018
Abstract Plenoptic images are highly demanded for 3D representation of broad scenes. Contrary to the images captured by conventional cameras, plenoptic images carry a considerable amount of angular information, which is very appealing for 3D reconstruction and display of the scene. Plenoptic images are gaining increasing importance in areas like medical imaging, manufacturing control, metrology, or even entertainment business. Thus, the adaptation and refinement of watermarking techniques to plenoptic images is a matter of raising interest. In this paper a new method for plenoptic image watermarking is proposed. A secret key is used to specify the location of logo insertion. Employing discr…
Towards an Efficient Implementation of an Accurate SPH Method
2020
A modified version of the Smoothed Particle Hydrodynamics (SPH) method is considered in order to overcome the loss of accuracy of the standard formulation. The summation of Gaussian kernel functions is employed, using the Improved Fast Gauss Transform (IFGT) to reduce the computational cost, while tuning the desired accuracy in the SPH method. This technique, coupled with an algorithmic design for exploiting the performance of Graphics Processing Units (GPUs), makes the method promising, as shown by numerical experiments.