Related papers: Better numerical approximation by Durrmeyer type o…
Unlike the classical polynomial case there has not been invented up to very recently a tool similar to the Bernstein-Bezier representation which would allow us to control the behavior of the exponential polynomials. The exponential analog…
We study the convergence of a family of numerical integration methods where the numerical integral is formulated as a finite matrix approximation to a multiplication operator. For bounded functions, the convergence has already been…
We give some new characterizations of strictly Lipschitz p-summing operators. These operators have been introduced in order to improve the Lipschitz p-summing operators. Therefore, we adapt this definition for constructing other classes of…
Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A progress to go beyond convexity was made by considering the…
In this paper, we introduce a new family of Szasz-Mirakyan-Durrmeyer operators defined on the half-line [0,\infty), constructed using Laguerre-type kernels. We discuss in detail the algebraic structure and analytical properties of these…
Quantum kernels are reproducing kernel functions built using quantum-mechanical principles and are studied with the aim of outperforming their classical counterparts. The enthusiasm for quantum kernel machines has been tempered by recent…
Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…
An analogue of Taylor's formula, which arises by substituting the classical derivative by a divided difference operator of Askey-Wilson type, is developed here. We study the convergence of the associated Taylor series. Our results…
A class of algorithms comprised by certain semismooth Newton and active-set methods is able to solve convex minimization problems involving sparsity-inducing regularizers very rapidly; the speed advantage of methods from this class is a…
In this paper we analyze a class of nonconvex optimization problem from the viewpoint of abstract convexity. Using the respective generalizations of the subgradient we propose an abstract notion proximal operator and derive a number of…
This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…
Motivated by a geometric meaning of Mahler's measure, we introduce two operator analogues of Mahler's measure. This leads to some interesting equalities and inequalities between the two operator-theoretic Mahler measures and the classical…
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Our approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine…
Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the…
A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…
In this article, we propose new proportional fractional operators generated from local proportional derivatives of a function with respect to another function. We present some properties of these fractional operators which can be also…
A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration…