Related papers: Monotone cubic spline interpolation for functions …
On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation. After presenting the natural extension of cubic splines to the Wasserstein space, we…
A new efficient orthogonalization of the B-spline basis is proposed and contrasted with some previous orthogonalized methods. The resulting orthogonal basis of splines is best visualized as a net of functions rather than a sequence of them.…
In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In…
Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
Gaussian kernels can be an efficient and accurate tool for multivariate interpolation. In practice, high accuracies are often achieved in the flat limit where the interpolation matrix becomes increasingly ill-conditioned. Stable evaluation…
High-dimensional/high-fidelity nonlinear dynamical systems appear naturally when the goal is to accurately model real-world phenomena. Many physical properties are thereby encoded in the internal differential structure of these resulting…
For the space $\mathcal{S}$ of $C^3$ quintics on the Powell-Sabin 12-split of a triangle, we determine the simplex splines in $\mathcal{S}$ and the six symmetric simplex spline bases that reduce to a B-spline basis on each edge, have a…
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…
This paper presents new fast algorithms for Hermite interpolation and evaluation over finite fields of characteristic two. The algorithms reduce the Hermite problems to instances of the standard multipoint interpolation and evaluation…
Several results on constrained spline smoothing are obtained. In particular, we establish a general result, showing how one can constructively smooth any monotone or convex piecewise polynomial function (ppf) (or any $q$-monotone ppf,…
In this paper we discuss the variety of planar spiral segments and their applications in objects in both the real and artificial world. The discussed curves with monotonic curvature function are well-known in geometric modelling and…
An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities…
We study a new simple quadrature rule based on integrating a $C^1$ quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions. We also give error estimates for smooth functions…
Duchon's method of thin plate splines defines a polyharmonic interpolant to scattered data values as the minimizer of a certain integral functional. For transfinite interpolation, i.e. interpolation of continuous data prescribed on curves…
In this paper we introduce a new class of diffeomorphic smoothers based on general spline smoothing techniques and on the use of some tools that have been recently developed in the context of image warping to compute smooth diffeomorphisms.…
In the space of all entire functions it is solved the problem of interpolation taking into account multiplicities by sums of the series of exponentials with the exponents from a given set. It is found a criterion of solubility of the…
In many classification problems it is desirable to output well-calibrated probabilities on the different classes. We propose a robust, non-parametric method of calibrating probabilities called SplineCalib that utilizes smoothing splines to…
Spherical functions appear throughout computer graphics, from spherical harmonic lighting and precomputed radiance transfer to neural radiance fields and procedural planet rendering. Efficient evaluation is critical for real-time…
We propose a method for interpolating divergence-free continuous magnetic fields via vector potential reconstruction using Hermite interpolation, which ensures high-order continuity for applications requiring adaptive, high-order ordinary…