Search results for "Numerical analysis"
showing 10 items of 883 documents
Upper bounds for the zeros of ultraspherical polynomials
1990
AbstractFor k = 1, 2, …, [n2] let xnk(λ) denote the Kth positive zero in decreasing order of the ultraspherical polynomial Pn(λ)(x). We establish upper bounds for xnk(λ). All the bounds become exact when λ = 0 and, in some cases (see case (iii) of Theorem 3.1), also when λ = 1. As a consequence of our results, we obtain for the largest zero xn1(λ)0.. We point out that our results remain useful for large values of λ. Numerical examples show that our upper bounds are quite sharp.
Mixed Convolutions and Zak Transforms
2015
In this chapter we introduce the mixed continuous–discrete and discrete–discrete convolutions. Important special cases of such convolutions are the polynomial and discrete splines, respectively. The Zak transforms, which are introduced in the chapter, provide integral representation of signals, which, in the following chapters, serves as a tool for the design of splines and spline-wavelets and operations over them. The exponential splines, which are the Zak transforms of polynomial and discrete B-splines are introduced. Explicit formulas for the characteristic functions of splines’ spaces are derived.
Estimates for the first and second Bohr radii of Reinhardt domains
2004
AbstractWe obtain general lower and upper estimates for the first and the second Bohr radii of bounded complete Reinhardt domains in Cn.
Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions
2013
AbstractNumerical solutions of the laminar Prandtl boundary-layer and Navier–Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. The various viscous–inviscid interactions that occur during the unsteady separation process are investigated by applying complex singularity analysis to the wall shear and streamwise velocity component of the two solutions. This is carried out using two different methodologies, namely a singularity-tracking method and the Padé approximation. It is shown how the van Dommelen and Shen singularity that occurs in solutions of the Prandtl boundary-layer equations evolves in the complex plane be…
An Efficient Numerical Method for Time Domain Computational Electromagnetic Simulation
2018
In this paper an efficient numerical method in approximating the electric and magnetic fields is provided. The method is based on an implicit leapfrog arrangement in time and without mesh in space. Moreover, a projection scheme is introduced in order to improve the accuracy of the proposed approach and applied into the computational electromagnetic (CEM) framework. The PDEs governing the process are solved and some numerical results are reported to validate the numerical process.
Approaches to evaluate the virtual instrumentation measurement uncertainties
2002
This paper deals with the metrological characterization of virtual instruments. After a brief description of the features, the components and the working principle of the virtual instruments and the various uncertainty sources are analyzed. Then, two methods to evaluate the uncertainty of the measurement results are presented: a numerical method simulating the physical process of the A/D conversion, and an approximated theoretical method applying the "uncertainty propagation law" of the "guide to the expression of uncertainty in measurement." With both methods, the combined standard uncertainty of the measurement result is obtained, starting from the standard uncertainty generated by each s…
Assessment of virtual instruments measurement uncertainty
2001
Abstract In this paper, two methods to evaluate the measurement uncertainty of a virtual instrument are presented: a numerical method simulating the physical process of the A/D conversion, and an approximated theoretical method applying the “uncertainty propagation law” of the “guide to the expression of uncertainty in measurement”. After a brief description of the features, the constitution and the working principle of the virtual instruments, the various uncertainty sources, are analyzed. With both methods, the combined standard uncertainty of the measurement result is obtained, starting from the standard uncertainty generated by each single source and without taking into account the para…
Perturbed Bernstein-type operators
2018
The present paper deals with modifications of Bernstein, Kantorovich, Durrmeyer and genuine Bernstein-Durrmeyer operators. Some previous results are improved in this study. Direct estimates for these operators by means of the first and second modulus of continuity are given. Also the asymptotic formulas for the new operators are proved.
Elementary hypergeometric functions, Heun functions, and moments of MKZ operators
2019
We consider some hypergeometric functions and prove that they are elementary functions. Consequently, the second order moments of Meyer-Konig and Zeller type operators are elementary functions. The higher order moments of these operators are expressed in terms of elementary functions and polylogarithms. Other applications are concerned with the expansion of certain Heun functions in series or finite sums of elementary hypergeometric functions.
Further results on generalized centro-invertible matrices
2019
[EN] This paper deals with generalized centro-invertible matrices introduced by the authors in Lebtahi et al. (Appl. Math. Lett. 38, 106¿109, 2014). As a first result, we state the coordinability between the classes of involutory matrices, generalized centro-invertible matrices, and {K}-centrosymmetric matrices. Then, some characterizations of generalized centro-invertible matrices are obtained. A spectral study of generalized centro-invertible matrices is given. In addition, we prove that the sign of a generalized centro-invertible matrix is {K}-centrosymmetric and that the class of generalized centro-invertible matrices is closed under the matrix sign function. Finally, some algorithms ha…