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The unconstrained minimization of a sufficiently smooth objective function $f(x)$ is considered, for which derivatives up to order $p$, $p\geq 2$, are assumed to be available. An adaptive regularization algorithm is proposed that uses…
We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…
We give an algorithm for the class of second order unification problems in which second order variables have at most one occurrence.
In this paper we obtain degree of approximation of functions in Lp by operators associated with their Fourier series using integral modulus of continuity. These results generalize many know results and are proved under less stringent…
Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between-class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two…
We extend the framework for complexity of operators in analysis devised by Kawamura and Cook (2012) to allow for the treatment of a wider class of representations. The main novelty is to endow represented spaces of interest with an…
We find asymptotic equalities for exact upper bounds of approximations by Fourier sums in uniform metric on classes of $2\pi$-periodic functions, representable in the form of convolutions of functions $\varphi$, which belong to unit balls…
We establish quantitative second-order Sobolev regularity for functions having a $2$-integrable $p$-Laplacian in bounded RCD spaces, with $p$ in a suitable range. In the finite-dimensional case, we also obtain Lipschitz regularity under the…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
We formulate some special conditions for the integrable functions and moduli of continuity. We give the results on rate of approximation of such functions by matrix means of their Fourier series, where the entries of the rows of the matrix…
Automating algorithm configuration is growing increasingly necessary as algorithms come with more and more tunable parameters. It is common to tune parameters using machine learning, optimizing performance metrics such as runtime and…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
By Fagin's Theorem, NP contains precisely those problems that can be described by formulas starting with an existential second-order quantifier, followed by only first-order quantifiers (ESO formulas). Subsequent research refined this…
In generalized Lebesgue spaces L^{p(.)} with variable exponent p(.) defined on the real axis, we obtain several inequalities of approximation by integral functions of finite degree. Approximation properties of Bernstein singular integrals…
The theory of boundary regularity for $p$-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality, $1<p<\infty$. The barrier classification of regular…
In this paper, exact rate of approximation of functions by linear means of Fourier series and Fourier integrals and corresponding $K$-functionals are expressed via special moduli of smoothness. . Introduction is given in $\S 1$. In $\S2$…
Being motivated by general interest as well as by certain concrete problems of Fourier Analysis, we construct analogs of the Lp spaces for measures. It turns out that most of standard properties of the usual Lp spaces for functions are…
Parallel parameterized complexity theory studies how fixed-parameter tractable (fpt) problems can be solved in parallel. Previous theoretical work focused on parallel algorithms that are very fast in principle, but did not take into account…
In metrics of spaces $L_{s}, \ 1\leq s\leq\infty$, we find asymptotic equalities for upper bounds of approximations by Fourier sums on classes of generalized Poisson integrals of periodic functions, which belong to unit ball of space…
In this paper, we obtain results about the positive definiteness, the continuity and the level-boundedness of two optimal value functions of specific parametric optimization problems. Those two optimization problems are generalizations of…