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The need to approximate functions is ubiquitous in science, either due to empirical constraints or high computational cost of accessing the function. In high-energy physics, the precise computation of the scattering cross-section of a…

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…

We study the local approximation properties in hierarchical spline spaces through multiscale quasi-interpolation operators. This construction suggests the analysis of a subspace of the classical hierarchical spline space (Vuong et al.,…

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…

It's well know that Radial Basis Function approximants suffers of bad conditioning if the simple basis of translates is used. A recent work of M.Pazouki and R.Schaback gives a quite general way to build stable, orthonormal bases for the…

In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. In order to complete the boundary of the patch a second spline…

Implicit 3D surface reconstruction of an object from its partial and noisy 3D point cloud scan is the classical geometry processing and 3D computer vision problem. In the literature, various 3D shape representations have been developed,…

We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…

Classical Laguerre spectral approximations are highly effective on the half-line when the target function is smooth in the usual polynomial scale. However, their accuracy deteriorates for nonsmooth functions. Such behavior appears naturally…

We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.

We provide a description of the interpolating and sampling sequences on a space of holomorphic functions with a uniform growth restriction defined on finite Riemann surfaces.

In mesh-based numerical simulations, the interpolation of mesh-defined functions across different meshes is a critical task, and achieving high-precision interpolation is of great significance for improving the computational efficiency and…

Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…

In this paper we consider the question of smoothness of slowly varying functions satisfying the modern definition that, in the last two decades, gained prevalence in the applications concerning function spaces and interpolation. We show,…

We obtain a result concerning the stability under the interpolation with functional parameter method for the approximation spaces of Lorentz-Marcinkiewicz type and also for the approximation spaces generated by symmetric norming functions…

In this paper a fourth order asymptotically optimal error bound for a new cubic interpolating spline function, denoted by Q-spline, is derived for the case that only function values at given points are used but not any derivative…

The spatial random-effects model is flexible in modeling spatial covariance functions, and is computationally efficient for spatial prediction via fixed rank kriging. However, the success of this model depends on an appropriate set of basis…

Recently, in [Electronic Transaction on Numerical Analysis, 41 (2014), pp. 420-442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional…

Radial basis functions are typically used when discretization sche-mes require inhomogeneous node distributions. While spawning from a desire to interpolate functions on a random set of nodes, they have found successful applications in…

This article aims to study fractal interpolation functions corresponding to a sequence of iterated function systems (IFSs). For a suitable choice of a sequence of IFS parameters, the corresponding non-stationary fractal function is a better…