Related papers: ENO reconstruction and ENO interpolation are stabl…
In this paper, we study the polynomial stability of analytical solution and convergence of the semi-implicit Euler method for non-linear stochastic pantograph differential equations. Firstly, the sufficient conditions for solutions to grow…
A novel central weighted essentially non-oscillatory (central WENO; CWENO)-type scheme for the construction of high-resolution approximations to discontinuous solutions to hyperbolic systems of conservation laws is presented. This procedure…
This paper introduces recovery thresholding hyperinterpolations, a novel class of methods for sparse signal reconstruction in the presence of noise. We develop a framework that integrates thresholding operators--including hard thresholding,…
In this paper, A new sixth-order weighted essentially non-oscillatory (WENO) scheme, refered as the WENO-6, is proposed in the finite volume framework for the hyperbolic conservation laws. Instead of selecting one stencil for each cell in…
The paper presents an in-depth exploration of the multinode Shepard interpolant on a regular rectangular grid, demonstrating its efficacy in reconstructing surfaces from DEM data. Additionally, we study the approximation order associated to…
Multirate behavior of ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) is characterized by widely separated time constants in different components of the solution or different additive terms of the…
Recombination is introduced into Eigen's theory of quasispecies evolution. Comparing numerical simulations of the rate equations in the non-recombining and recombining cases show that recombination has a strong effect on the error threshold…
Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise…
The recently proposed high-order TENO scheme [Fu et al., Journal of Computational Physics, 305, pp.333-359] has shown great potential in predicting complex fluids owing to the novel weighting strategy, which ensures the high-order accuracy,…
Neural ordinary differential equations (neural ODEs) have emerged as a natural tool for supervised learning from a control perspective, yet a complete understanding of their optimal architecture remains elusive. In this work, we examine the…
The number of algorithms available to reconstruct a biological network from a dataset of high-throughput measurements is nowadays overwhelming, but evaluating their performance when the gold standard is unknown is a difficult task. Here we…
Given a level set $E$ of an arbitrary multiplicative function $f$, we establish, by building on the fundamental work of Frantzikinakis and Host [13,14], a structure theorem which gives a decomposition of $\mathbb{1}_E$ into an almost…
The aim of this paper is to propose for the first time a reconstruction scheme and a stability result for recovering from acoustic-optic data absorption distributions with bounded variation. The paper extends earlier results on smooth…
This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction…
In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based method that,…
Common smoothness indicators used in Weighted Essentially Non\--Os\-cil\-la\-to\-ry (WENO) reconstructions [Jiang, G.S., Shu, C.W.: Efficient implementation of {Weighted} {ENO} schemes, J.\ Comput.\ Phys. \textbf{126}, 202--228 (1996)] have…
In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced…
In the 1-dimensional multiple changepoint detection problem, we prove that any procedure with a fast enough $\ell_2$ error rate, in terms of its estimation of the underlying piecewise constant mean vector, automatically has an (approximate)…
We develop two new ideas for interpolation on $\mathbb{S}^2$. In this first part, we will introduce a simple interpolation method named \textit{Spherical Interpolation of orDER} $n$ (SIDER-$n$) that gives a $C^{n}$ interpolant given $n \geq…
We present a new analysis of the stability of extended Floater-Hormann interpolants, in which both noisy data and rounding errors are considered. Contrary to what is claimed in the current literature, we show that the Lebesgue constant of…