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Volume 81, Issue CApr 2024
Publisher:
  • Academic Press, Inc.
  • 6277 Sea Harbor Drive Orlando, FL
  • United States
ISSN:0885-064X
Reflects downloads up to 20 Dec 2024Bibliometrics
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research-article
Optimal recovery and generalized Carlson inequality for weights with symmetry properties
Abstract

The paper concerns problems of the recovery of operators from noisy information in weighted  L q-spaces with homogeneous weights. A number of general theorems are proved and applied to finding exact constants in multidimensional Carlson type ...

research-article
The minimal radius of Galerkin information for the problem of numerical differentiation
Abstract

The problem of numerical differentiation for periodic functions with finite smoothness is investigated. For multivariate functions, different variants of the truncation method are constructed and their approximation properties are obtained. Based ...

research-article
On a unified convergence analysis for Newton-type methods solving generalized equations with the Aubin property
Abstract

A plethora of applications from diverse disciplines reduce to solving generalized equations involving Banach space valued operators. These equations are solved mostly iteratively, when a sequence is generated approximating a solution provided ...

research-article
A duality approach to regularized learning problems in Banach spaces
Abstract

Regularized learning problems in Banach spaces, which often minimize the sum of a data fidelity term in one Banach norm and a regularization term in another Banach norm, is challenging to solve. We construct a direct sum space based on the Banach ...

research-article
Randomized complexity of parametric integration and the role of adaption I. Finite dimensional case
Abstract

We study the randomized n-th minimal errors (and hence the complexity) of vector valued mean computation, which is the discrete version of parametric integration. The results of the present paper form the basis for the complexity analysis of ...

research-article
On the information complexity for integration in subspaces of the Wiener algebra
Abstract

Recently, Goda proved the polynomial tractability of integration on the following function subspace of the Wiener algebra F d : = { f ∈ C ( T d ) | ‖ f ‖ F d : = ∑ k ∈ Z d | f ˆ ( k ) | max ⁡ ( 1 , min j ∈ supp ( k ) ⁡ log ⁡ | k j | ) < ∞ } , ...

research-article
Complexity for a class of elliptic ordinary integro-differential equations
Abstract

Consider the variational form of the ordinary integro-differential equation (OIDE) − u ″ + u + ∫ 0 1 q ( ⋅ , y ) u ( y ) dy = f on the unit interval I, subject to homogeneous Neumann boundary conditions. Here, f and q respectively belong to the ...

research-article
Sharp lower error bounds for strong approximation of SDEs with piecewise Lipschitz continuous drift coefficient
Abstract

We study pathwise approximation of strong solutions of scalar stochastic differential equations (SDEs) at a single time in the presence of discontinuities of the drift coefficient. Recently, it has been shown by Müller-Gronbach and Yaroslavtseva (...

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