Related papers: Splinets -- efficient orthonormalization of the B-…
A piecewise Chebyshevian spline space is a space of spline functions having pieces in different Extended Chebyshev spaces and where the continuity conditions between adjacent spline segments are expressed by means of connection matrices.…
Given a spline space spanned by Truncated Hierarchical B-splines (THB), it is always possible to construct a spline space spanned by Locally Refined B-splines (LRB) that contains the THB-space. Starting from configurations where the two…
Locally refined spline surfaces (LRB) is a representation well suited for scattered data approximation. When a data set has local details in some areas and is largely smooth in other, LR B-splines allow the spatial distribution of degrees…
We study nonlinear approximation in $\operatorname{BMO}$ from splines generated by a hierarchy of B-splines over regular multilevel nested partitions of $\mathbb R$. Companion Jackson and Bernstein estimates are established that allow to…
In this paper, a method is proposed to solve the problem of monotone smoothing splines using general linear systems. This problem, also called monotone control theoretic splines, has been solved only when the curve generator is modeled by…
Slender-body approximations have been successfully used to explain many phenomena in low-Reynolds number fluid mechanics. These approximations typically use a line of singularity solutions to represent the flow. These singularities can be…
We propose an improvement of the basis for the solution of the stationary two-centre Dirac equation in Cassini coordinates using the finite-basis-set method presented in Ref. [1]. For the calculations in Ref. [1], we constructed the basis…
We use Lorentz polynomials to present the solutions explicitly of equations (6.1.7) of [I. Daubechies, Ten lectures on wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, 61. Society for Industrial and Applied Mathematics…
In this paper we study dual bases functions in subspaces. These are bases which are dual to functionals on larger linear space. Our goal is construct and derive properties of certain bases obtained from the construction, with primary focus…
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…
The skyrmion, which is characterised by a topological integer, is a structure that is topologically stable against local disturbances. The huge potential of skyrmions for use in magnetic storage systems has drawn considerable research…
A new global basis of B-splines is defined in the space of generalized quadratic splines (GQS) generated by Merrien subdivision algorithm. Then, refinement equations for these B-splines and the associated corner-cutting algorithm are given.…
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…
In this paper, we develop a robust efficient visual SLAM system that utilizes heterogeneous point and line features. By leveraging ORB-SLAM [1], the proposed system consists of stereo matching, frame tracking, local mapping, loop detection,…
Spline wavelet tight frames of Ron-Shen have been used widely in frame based image analysis and restorations. However, except for the tight frame property and the approximation order of the truncated series, there are few other properties…
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…
We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localised basis functions of different shapes, which we…
We introduce discrete analogues of the exponential, sine, and cosine functions. Then using a discrete trigonometric version of a non-polynomial divided difference, we define discrete analogues of the trigonometric B-splines. We derive a…
The method of constructing trigonometric Hermite splines, which interpolate the values of some periodic function and its derivatives in the nodes of a uniform grid, is considered. The proposed method is based on the periodicity properties…
To deal with non-linear relations between the predictors and the response, we can use transformations to make the data look linear or approximately linear. In practice, however, transformation methods may be ineffective, and it may be more…