Related papers: Scalar Compandor Design Based on Optimal Compresso…
In this paper, the approximation of the optimal compressor function using spline function of the first-degree is done. For the companding quantizer designed on the basis of the approximative spline function of the first-degree, the support…
In this paper, an approximation of the optimal compressor function using the quadratic spline functions has been presented. The coefficients of the quadratic spline functions are determined by minimizing the mean-square error (MSE). Based…
To overcome the difficulties in determining an inverse compressor function for a Gaussian source, which appear in designing the nonlinear optimal companding quantizers and also in the nonlinear optimal companding quantization procedure, in…
In this paper both piecewise linear and piecewise uniform approximation of probability density function are performed. For the probability density function approximated in these ways, a compressor function is formed. On the basis of…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
The goal of this paper is to design compact support basis spline functions that best approximate a given filter (e.g., an ideal Lowpass filter). The optimum function is found by minimizing the least square problem ($\ell$2 norm of the…
The perimeter and area generating functions of exactly solvable polygon models satisfy q-functional equations, where q is the area variable. The behaviour in the vicinity of the point where the perimeter generating function diverges can…
In this paper, we present new quasi-interpolating spline schemes defined on 3D bounded domains, based on trivariate $C^2$ quartic box splines on type-6 tetrahedral partitions and with approximation order four. Such methods can be used for…
In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…
Devising optimal operating strategies for a compressor station relies on the knowledge of compressor characteristics. As the compressor characteristics change with time and use, it is necessary to provide accurate models of the…
We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size $n$, the smoothing spline estimator can be expressed as a linear combination of $n$ basis functions,…
Approximating data points in three or higher dimension space based on cubic B-spline curve is presented. Representations for planar curves, are merged and extended to the higher dimension. The curve is fitted to the order of data points, or…
We present a procedure to approximate a plane contour by piecewise polynomial functions, depending on various parameters, such as degree, number of local patches, selection of knots. This procedure aims to be adopted to study how…
Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of a…
Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to…
This paper studies function approximation in Gaussian Sobolev spaces over the real line and measures the error in a Gaussian-weighted $L^p$-norm. We construct two linear approximation algorithms using $n$ function evaluations that achieve…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
This paper deals with a linear model of regression on quantiles when the explanatory variable takes values in some functional space and the response is scalar. We propose a spline estimator of the functional coefficient that minimizes a…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is…