Optimal recovery and generalized Carlson inequality for weights with symmetry properties
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 ...
The minimal radius of Galerkin information for the problem of numerical differentiation
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 ...
On a unified convergence analysis for Newton-type methods solving generalized equations with the Aubin property
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 ...
A duality approach to regularized learning problems in Banach spaces
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 ...
On the information complexity for integration in subspaces of the Wiener algebra
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 | ) < ∞ } , ...
Complexity for a class of elliptic ordinary integro-differential equations
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 ...
Sharp lower error bounds for strong approximation of SDEs with piecewise Lipschitz continuous drift coefficient
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 (...