Related papers: Approximation error estimates and inverse inequali…
Tile B-splines in $\mathbb{R}^d$ are defined as autoconvolutions of the indicators of tiles, which are special self-similar compact sets whose integer translates tile the space $\mathbb{R}^d$. These functions are not piecewise-polynomial,…
Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…
Adaptive approximation (or interpolation) takes into account local variations in the behavior of the given function, adjusts the approximant depending on it, and hence yields the smaller error of approximation. The question of constructing…
An interior penalty discontinuous Galerkin method is devised to approximate minimizers of a linear folding model by discontinuous isoparametric finite element functions that account for an approximation of a folding arc. The numerical…
In this paper we establish the reversed sharp Hardy-Littlewood-Sobolev (HLS for short) inequality on the upper half space and obtain a new HLS type integral inequality on the upper half space (extending an inequality found by Hang, Wang and…
Location estimation is a central problem in functional data analysis. In this paper, we investigate penalized spline estimators of location for discretely sampled functional data under a broad class of convex loss functions. Our framework…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
We consider best approximation problems in a nonlinear subset $\mathcal{M}$ of a Banach space of functions $(\mathcal{V},\|\bullet\|)$. The norm is assumed to be a generalization of the $L^2$-norm for which only a weighted Monte Carlo…
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By…
A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in [11]. We show in this paper how it can be used to solve the fault inverse problem, where a planar fault in elastic half-space and a slip on…
In this paper, we propose to use the general $L^2$-based Sobolev norms, i.e., $H^s$ norms where $s\in \mathbb{R}$, to measure the data discrepancy due to noise in image processing tasks that are formulated as optimization problems. As…
Exact-order estimates are obtained for some approximation characteristics of the classes of periodic multivariate functions with mixed smoothness (the Nikol'skii-Besov classes $B^{\boldsymbol{r}}_{p, \theta}$) in the space $B_{q,1}$, $1…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
A convincing feature of least-squares finite element methods is the built-in a posteriori error estimator for any conforming discretization. In order to generalize this property to discontinuous finite element ansatz functions, this paper…
In this paper, both semidiscrete and completely discrete finite volume element methods (FVEMs) are analyzed for approximating solutions of a class of linear hyperbolic integro- differential equations in a two-dimensional convex polygonal…
Fixed a continuous kernel K on the $d$-dimensional torus, we consider a generalization of the univariate $sk$-spline to the torus, associated with the kernel K. It is proved an estimate which provides the rate of convergence of a given…
This work develops polynomial-degree-robust (p-robust) equilibrated a posteriori error estimates for $H(\rm curl)$, $H(\rm div)$ and $H(\rm divdiv)$ problems, based on $H^1$ auxiliary space decomposition. The proposed framework employs…
We first give a general error estimate for the nonconforming approximation of a problem for which a Banach-Ne{\v c}as-Babu{\v s}ka (BNB) inequality holds. This framework covers parabolic problems with general conditions in time (initial…
In this paper we provide some error estimates for the div least-squares finite element method on elliptic problems. The main contribution is presenting a complete error analysis, which improves the current \emph{state-of-the-art} results.…
Krylov subspace methods are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we study the approximation quality that a Krylov subspace provides for estimating the numerical range of a matrix.…