Related papers: Sinc approximation of algebraically decaying funct…
In this paper we consider the approximation of functions by radial basis function interpolants. There is a plethora of results about the asymptotic behaviour of the error between appropriately smooth functions and their interpolants, as the…
We study in this paper the function approximation error of linear interpolation and extrapolation. Several upper bounds are presented along with the conditions under which they are sharp. All results are under the assumptions that the…
We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.
Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same…
In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
A new sampling methodology based on incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the…
Based on two point spline approximations of arbitrary order, a series of functions that define lower bounds for sin(x) and sin(x)/x, over the interval [0,Pi/2], with increasingly low relative errors and smaller relative errors than…
This paper deals with probabilistic upper bounds for the error in functional estimation defined on some interpolation and extrapolation designs, when the function to estimate is supposed to be analytic. The error pertaining to the estimate…
This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…
In this paper, two double Jordan-type inequalities are introduced that generalize some previously established inequalities. As a result, some new upper and lower bounds and approximations of the sinc function are obtained. This extension of…
We adapt Schaback's error doubling trick [R. Schaback. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp., 68(225):201--216, 1999.] to give error estimates for radial interpolation of functions…
We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.
This article presents novel proof methods for estimating interpolation errors, predicated on the understanding that one has already studied foundational error analysis using the finite element method.
In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange…
In this paper we prove some exponential inequalities involving the sinc function. We analyze and prove inequalities with constant exponents as well as inequalities with certain polynomial exponents. Also, we establish intervals in which…
Interpolation by various types of splines is the standard procedure in many applications. In this paper we shall discuss harmonic spline "interpolation" (on the lines of a grid) as an alternative to polynomial spline interpolation (at…
In this paper, we study several degenerate trigonometric functions, which are degenerate versions of the ordinary trigonometric functions, and derive some identities among such functions by using elementary methods. Especially, we obtain…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
Different types of sinc integrals are investigated when the standard sine function is replaced by the generalised $\sin_{p,q}$ in two parameters. A striking generalisation of the improper Dirichlet integral is achieved. A second surprising…