Related papers: AutoKnots: Adaptive Knot Allocation for Spline Int…
Regression splines are smooth, flexible, and parsimonious nonparametric function estimators. They are known to be sensitive to knot number and placement, but if assumptions such as monotonicity or convexity may be imposed on the regression…
Global 21-cm experiments are built to study the evolution of the Universe between the cosmic dawn and the epoch of reionisation. FlexKnot is a function parameterised by freely moving knots stringed together by splines. Adopting the FlexKnot…
The efficient compression of kernel matrices, for instance the off-diagonal blocks of discretized integral equations, is a crucial step in many algorithms. In this paper, we study the application of Skeletonized Interpolation to construct…
Robotic manipulation of deformable linear objects (DLOs) presents significant challenges due to complex dynamics and frequent self-occlusions. Existing robotic knot tying methods typically rely on precise topological state tracking with…
We study numerical integration of smooth functions defined over the $s$-dimensional unit cube. A recent work by Dick et al. (2019) has introduced so-called extrapolated polynomial lattice rules, which achieve the almost optimal rate of…
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…
This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…
A set of arbitrarily high-order WENO schemes for reconstructions on nonuniform grids is presented. These non-linear interpolation methods use simple smoothness indicators with a linear cost with respect to the order, making them easy to…
As the convolutional neural network (CNN) gets deeper and wider in recent years, the requirements for the amount of data and hardware resources have gradually increased. Meanwhile, CNN also reveals salient redundancy in several tasks. The…
I describe a new, open-source astronomical image-fitting program called Imfit, specialized for galaxies but potentially useful for other sources, which is fast, flexible, and highly extensible. A key characteristic of the program is an…
We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…
We present an algorithm to compute best least-squares approximations of discrete real-valued functions by first-degree splines (broken lines) with free knots. We demonstrate that the algorithm delivers after a finite number of steps a…
This paper describes the development of an automated knot selection method (selecting number and location of knots) for bivariate splines in a pure regression framework (SALSA2D). To demonstrate this approach we use carcass location data…
An algorithm for computing an analytic function of a matrix $A$ is described. The algorithm is intended for the case where $A$ has some close eigenvalues, and clusters (subsets) of close eigenvalues are separated from each other. This…
We study a class of nested path problems, in which every path-based variable can be decomposed into a sequence of subpaths. Subpaths must satisfy local resources, while paths must satisfy additional global resources. This paper develops a…
We introduce and publicly release a new code, ADAPTSMOOTH, which serves to smooth astronomical images in an adaptive fashion, in order to enhance the signal-to-noise ratio (S/N). The adaptive smoothing scheme allows to take full advantage…
While there exists a rich array of matrix column subset selection problem (CSSP) algorithms for use with interpolative and CUR-type decompositions, their use can often become prohibitive as the size of the input matrix increases. In an…
This paper introduces an astronomical image alignment algorithm. This algorithm uses the means of the rows and columns of the original image for alignment, and finds the optimal offset corresponding to the maximum similarity by comparing…
We present a method for dimensionally adaptive sparse trigonometric interpolation of multidimensional periodic functions belonging to a smoothness class of finite order. This method targets applications where periodicity must be preserved…
Anomaly detection of time series plays an important role in reliability systems engineering. However, in practical application, there is no precisely defined boundary between normal and anomalous behaviors in different application…