相关论文: Peaks and jumps reconstruction with B-splines scal…
We propose a numerical method to spline-interpolate discrete signals and then apply the integral transforms to the corresponding analytical spline functions. This represents a robust and computationally efficient technique for estimating…
We consider the 1D cubic NLS on $\mathbb R$ and prove a blow-up result for functions that are of borderline regularity, i.e. $H^s$ for any $s<-\frac 12$ for the Sobolev scale and $\mathcal F L^\infty$ for the Fourier-Lebesgue scale. This is…
This paper presents a PDE-based planar parameterization framework with support for Truncated Hierarchical B-Splines (THB-splines). For this, we adopt the a posteriori refinement strategy of Dual Weighted Residual and present several…
We present a constructive approximation framework for analyzing the expressive power of Fourier residual networks in approximating a broad class of one-dimensional functions. Our study covers both piecewise continuous functions -- including…
Recovering frequency-localized functions from pointwise data is a fundamental task in signal processing. We examine this problem from an approximation-theoretic perspective, focusing on least squares and deep learning-based methods. First,…
This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…
The aim of this paper is to present the new results concerning some functionals of Brownian motion with drift and present their applications in financial mathematics. We find a probabilistic representation of the Laplace transform of…
The inversion problem for rational B\'ezier curves is addressed by using resultant matrices for polynomials expressed in the Bernstein basis. The aim of the work is not to construct an inversion formula but finding the corresponding value…
We construct an approximate renormalization for Hamiltonian systems with two degrees of freedom in order to study the break-up of invariant tori with arbitrary frequency. We derive the equation of the critical surface of the renormalization…
Non-uniform B-spline dictionaries on a compact interval are discussed. For each given partition, dictionaries of B-spline functions for the corresponding spline space are constructed. It is asserted that, by dividing the given partition…
The popular cubic smoothing spline estimate of a regression function arises as the minimizer of the penalized sum of squares $\sum_j(Y_j - {\mu}(t_j))^2 + {\lambda}\int_a^b [{\mu}"(t)]^2 dt$, where the data are $t_j,Y_j$, $j=1,..., n$. The…
Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates.…
Normalizing flows have been successfully modeling a complex probability distribution as an invertible transformation of a simple base distribution. However, there are often applications that require more than invertibility. For instance,…
Mathematical methods of step-by-step and combined shifts are proposed for experimental data processing to reconstruct the measuring system impulse response distorted by shift-invariant blur. Proposed methods base on direct non-blind…
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.…
In functional linear regression, the slope ``parameter'' is a function. Therefore, in a nonparametric context, it is determined by an infinite number of unknowns. Its estimation involves solving an ill-posed problem and has points of…
We propose a class of numerical schemes for mixed optimal stopping and control of processes with infinite activity jumps and where the objective is evaluated by a nonlinear expectation. Exploiting an approximation by switching systems,…
In this paper, we propose a new horseshoe-type prior hierarchy for adaptively shrinking spline-based functional effects towards a predefined vector space of parametric functions. Instead of shrinking each spline coefficient towards zero, we…
We propose a variational form of the BDF2 method as an alternative to the commonly used minimizing movement scheme for the time-discrete approximation of gradient flows in abstract metric spaces. Assuming uniform semi-convexity --- but no…
Infinite-dimensional, holomorphic functions have been studied in detail over the last several decades, due to their relevance to parametric differential equations and computational uncertainty quantification. The approximation of such…