Related papers: On thin plate spline interpolation
The current implementation of Thiele rational interpolation in Maple (the ThieleInterpolation routine) breaks down when the points are not well-ordered. In this article, it is shown how this breakdown can be avoided by ordering the…
There are many methods for image enhancement. Image inpainting is one of them which could be used in reconstruction and restoration of scratch images or editing images by adding or removing objects. According to its application, different…
We consider shells in three dimensional Euclidean space which have bounded principal curvatures. We prove Korn's interpolation (or the so called first and a half\footnote{The inequality first introduced in [6]}) and second inequalities on…
We propose a polynomial preserving recovery method for PHT-splines within isogeometric analysis to obtain more accurate gradient approximations. The method fully exploits the local interpolation properties of PHT-splines and avoids the need…
A posteriori error estimates are derived in the context of two-dimensional structural elastic shape optimization under the compliance objective. It is known that the optimal shape features are microstructures that can be constructed using…
This note is an (exact) copy of the report of Jaak Peetre, "H-infinity and Complex Interpolation". Published as Technical Report, Lund (1981). Some more recent general references have been added, some references updated though (in italics)…
We present error estimates of the fully semi-Lagrangian scheme with high-order interpolation operators, solving the initial value problems for the one-dimensional nonlinear diffusive conservation laws, including the Burgers equations. We…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike…
A family of continuous piecewise linear finite elements for thin plate problems is presented. We use standard linear interpolation of the deflection field to reconstruct a discontinuous piecewise quadratic deflection field. This allows us…
In CAGD the design of a surface that interpolates an arbitrary quadrilateral mesh is definitely a challenging task. The basic requirement is to satisfy both criteria concerning the regularity of the surface and aesthetic concepts. With…
This note concerns the interpolation problem with two parametrized families of splines related to polynomial spline interpolation. We address the questions of uniqueness and establish basic convergence rates for splines of the form $…
We establish error estimates for semi-Lagrangian schemes for the initial value problem of one-dimensional conservation laws with a dispersive term, including the Korteweg--de Vries equation. The schemes considered in this paper are based on…
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.
Through-plane resolution in clinical MRI is typically much coarser than in-plane resolution, limiting diagnostic utility. This work investigates deep learning approaches to interpolate intermediate MRI slices in prostate imaging,…
In this work we blend interpolation theory with numerical integration, constructing an interpolator based on integrals over $n$-dimensional balls. We show that, under hypotheses on the radius of the $n$-balls, the problem can be treated as…
Smoothed particle hydrodynamics (SPH) discretization techniques are generalized to develop a method, smoothed particle interpolation (SPI), for solving initial value problems of systems of non-hydrodynamical nature. Under this approach, SPH…
In this paper, we build up a framework for sparse interpolation. We first investigate the theoretical limit of the number of unisolvent points for sparse interpolation under a general setting and try to answer some basic questions of this…
We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from…
Time delay estimation has long been an active area of research. In this work, we show that compressive sensing with interpolation may be used to achieve good estimation precision while lowering the sampling frequency. We propose an…