Related papers: Minimal Numerical Differentiation Formulas
We establish theoretical guarantees for the expected prediction error of the exponential weighting aggregate in the case of multivariate regression that is when the label vector is multidimensional. We consider the regression model with…
When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…
The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…
We suggest an efficient algorithm for the selection of sparse subsets of a set of influence for the numerical discretization of differential operators on irregular nodes with polynomial consistency of a given order with the help of the QR…
In the theory of error-correcting codes, the minimum weight and the weight enumerator play a crucial role in evaluating the error-correcting capacity. In this paper, by viewing the weight enumerator as a quasi-polynomial, we reduce the…
In this paper, we consider the affine variety codes obtained evaluating the polynomials $by=a_kx^k+\dots+a_1x+a_0$, $b,a_i\in\mathbb{F}_{q^r}$, at the affine $\F_{q^r}$-rational points of the Norm-Trace curve. In particular, we investigate…
Kernel smoothers are considered near the boundary of the interval. Kernels which minimize the expected mean square error are derived. These kernels are equivalent to using a linear weighting function in the local polynomial regression. It…
We present numerical upscaling techniques for a class of linear second-order self-adjoint elliptic partial differential operators (or their high-resolution finite element discretization). As prototypes for the application of our theory we…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
This article deals with error estimates for the finite element approximation of variational normal derivatives and, as a consequence, error estimates for the finite element approximation of Dirichlet boundary control problems with energy…
This paper considers estimation and inference in semiparametric econometric models. Standard procedures estimate the model based on an independence restriction that induces a minimum distance between a joint cumulative distribution function…
Statistical divergences (SDs), which quantify the dissimilarity between probability distributions, are a basic constituent of statistical inference and machine learning. A modern method for estimating those divergences relies on…
The paper studies a general norm minimization problem on a product of normed vector spaces. We establish dual necessary and sufficient optimality conditions and derive explicit formulas for the corresponding solution sets. These formulas…
We consider the problem of minimizing variational integrals defined on \cc{nonlinear} Sobolev spaces of competitors taking values into the sphere. The main novelty is that the underlying energy features a non-uniformly elliptic integrand…
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…
This article studies separating invariants for the ring of multisymmetric polynomials in $m$ sets of $n$ variables over an arbitrary field $\mathbb{K}$. We prove that in order to obtain separating sets it is enough to consider polynomials…
This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…
For numerical approximation the reformulation of a PDE as a residual minimisation problem has the advantages that the resulting linear system is symmetric positive definite, and that the norm of the residual provides an a posteriori error…