Related papers: sk-Spline interpolation on R^n
Periodic splines are a special kind of splines that are defined over a set of knots over a circle and are adequate for solving interpolation problems related to closed curves. This paper presents a method of implementing the objects…
This paper explores the generalization of the method for extracting Riemann trigonometric B-splines and Riemann kernels of trigonometric interpolation splines of arbitrary order on different grids of stitching and interpolation. It is…
A systematic construction of higher order splines using two hierarchies of polynomials is presented. Explicit instructions on how to implement one of these hierarchies are given. The results are limited to interpolations on regular,…
Using factorisation and Arov-Krein inequality results, we derive important inequalities (in terms of $S$-nodes) in interpolation problems.
Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches…
This article focuses on trigonometric Riemann B-splines and Riemann kernels of trigonometric interpolation splines of arbitrary order; it is shown that trigonometric interpolation splines are a convolution of trigonometric B-splines with…
The paper deals with two fundamental types of trigonometric polynomials and splines on uniform grids, which allow us to construct interpolation approximations that depend linearly on the values of the interpolated function. Fundamental on…
Spline functions have long been used in numerical solution of differential equations. Recently it revives as isogeometric analysis, which offers integration of finite element analysis and NURBS based CAD into a single unified process.…
One of the possible variants of the classification of trigonometric interpolation splines is considered, depending on the chosen convergence factors, the distribution of signs of the basis functions and the interpolation factors. The…
A class of trigonometric interpolation splines depending on parameter vectors, selected convergence factors and interpolation factors is considered. The concept of crosslink grids and interpolation grids is introduced; these grids can match…
Under consideration methods of constructing trigonometric interpolation splines of two variables on rectangular areas. These methods are easily generalized to the case of trigonometric interpolation splines of several variables on such…
Second order spiral splines are $C^2$ unit-speed planar curves that can be used to interpolate a list $Y$ of $n+1$ points in $\R ^2$ at times specified in some list $T$, where $n\geq 2$. Asymptotic methods are used to develop a fast…
Methods of constructing trigonometric fundamental splines with constant sign and sign-changing convergence factors are given. An example and graphics illustrating the concepts of convergence and interpolation grids are given. Some methods…
This paper addresses the problems of spline interpolation on smooth Riemannian manifolds, with or without the inclusion of least-squares fitting. Our unified approach utilizes gradient flows for successively connected curves or networks,…
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…
We extend the classical theory of variational interpolating splines to the case of compact Riemannian manifolds. Our consideration includes in particular such problems as interpolation of a function by its values on a discrete set of points…
This note is the updated outline of the article "Interpolational properties of planar spiral curves", Fund. and Applied Math., 2001, Vol.7, N.2, 441-463, published in Russian. The main result establishes boundary regions for spiral and…
We develop a local polynomial spline interpolation scheme for arbitrary spline order on bounded intervals. Our method's local formulation, effective boundary considerations and optimal interpolation error rate make it particularly useful…
The class $Ts(r,f)$ the trigonometric interpolation splines depending on the parameter vectors, selected convergence factors and interpolation factors is considered. The main properties of simple interpolation trigonometric splines are…
Three forms of representation of trigonometric interpolation splines are considered, in particular, the representation by the coefficients of the interpolation trigonometric polynomial, the representation by trigonometric B-splines, which…