Related papers: On Tractability of Approximation for a Special Spa…
Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…
The extremum value theorem for function spaces plays the central role in optimal control. It is known that computation of optimal control actions and policies is often prone to numerical errors which may be related to computability issues.…
We study the average case complexity of a linear multivariate problem $(\lmp)$ defined on functions of $d$ variables. We consider two classes of information. The first $\lstd$ consists of function values and the second $\lall$ of all…
We present a new and compelling approach to the efficient solution of important computational problems that arise in the context of abstract argumentation. Our approach makes known algorithms defined for restricted fragments generally…
In this paper we consider $L_p$-approximation, $p \in \{2,\infty\}$, of periodic functions from weighted Korobov spaces. In particular, we discuss tractability properties of such problems, which means that we aim to relate the dependence of…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…
We study the $L_1$-approximation of $d$-variate monotone functions based on information from $n$ function evaluations. It is known that this problem suffers from the curse of dimensionality in the deterministic setting, that is, the number…
We investigate the approximation of $d$-variate periodic functions in Sobolev spaces of dominating mixed (fractional) smoothness $s>0$ on the $d$-dimensional torus, where the approximation error is measured in the $L_2-$norm. In other…
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
We present a lower error bound for approximating linear multivariate operators defined over Hilbert spaces in terms of the error bounds for appropriately constructed linear functionals as long as algorithms use function values. Furthermore,…
We consider multivariate integration in the randomized setting. The function spaces which we study are defined on R^s with respect to the Gaussian measure and the functions are characterized by the decay of their Hermite coefficients. We…
In this paper we consider integration and $L_2$-approximation for functions over $\RR^s$ from weighted Hermite spaces. The first part of the paper is devoted to a comparison of several weighted Hermite spaces that appear in literature,…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
The density of polynomials in a weighted space of infinitely differentiable functions in a multidimensional real space is proved under minimal conditions on weight functions and on differences between weight functions. We apply this result…
This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…
These notes contain, among others, a proof that the average running time of an easy solution to the satisfiability problem for propositional calculus is, under some reasonable assumptions, linear (with constant 2) in the size of the input.…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give estimates…