Related papers: Iterative operator-splitting methods for unbounded…
Bounded and unbounded weighted composition operators on $L^2$ spaces over $\sigma$-finite measure spaces are investigated. A variety of questions related to seminormality of such operators are discussed.
We propose a hierarchical splitting approach to differential equations that provides a design principle for constructing splitting methods for $N$-split systems by iteratively applying splitting methods for two-split systems. We analyze the…
Using oblique projections and angles between subspaces we write condition number estimates for abstract nonsymmetric domain decomposition methods. In particular, we consider a restricted additive method for the Poisson equation and write a…
In this work we give H\"older-Besov estimates for periodic Fourier multipliers. We present a class of bounded pseudo-differential operators on periodic Besov spaces with symbols of limited regularity.
This work focuses on the well-posedness of abstract stochastic linear systems with boundary input delay and unbounded observation operators. We use product spaces and a semigroup approach to reformulate such delay systems into free-delay…
Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. Although monolithic approaches offer possibly the best solution strategy, they often require ad-hoc preconditioners and…
Schr\"odinger operators with periodic (possibly complex-valued) potentials and discrete periodic operators (possibly with complex-valued entries) are considered, and in both cases the computational spectral problem is investigated: namely,…
In constraining iterative processes, the algorithmic operator of the iterative process is pre-multiplied by a constraining operator at each iterative step. This enables the constrained algorithm, besides solving the original problem, also…
We introduce a fast and scalable method for solving quadratic programs with conditional value-at-risk (CVaR) constraints. While these problems can be formulated as standard quadratic programs, the number of variables and constraints grows…
We prove bilinear inequalities for differential operators in $\mathbb{R}^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However,…
This article is devoted to the construction of numerical methods which remain insensitive to the smallness of the semiclassical parameter for the linear Schr{\"o}dinger equation in the semiclassical limit. We specifically analyse the…
The Iterative Filtering method is a technique developed recently for the decomposition and analysis of non-stationary and non-linear signals. In this work we propose two alternative formulations of the original algorithm which allows to…
We suggest a modification of the operator exponential method for the numerical solving the difference linear initial boundary value problems. The scheme is based on the representation of the difference operator for given boundary conditions…
In this work, we show high order splitting methods of integration without negative steps, allowing us to solve numerically irreversible problems, like reaction-diffusion equations. The methods consist in a suitable affine combinations of…
Qualitative and quantitative aspects for variational inequalities governed by strongly pseudomonotone operators on Hilbert space are investigated in this paper. First, we establish a global error bound for the solution set of the given…
We explore the applicability of splitting methods involving complex coefficients to solve numerically the time-dependent Schr\"odinger equation. We prove that a particular class of integrators are conjugate to unitary methods for…
Spectral components of one-dimensional Schr\"odinger operator with complex potential are investigated. An effective upper bound for the total number of eigenvalues and spectral singularities is established. For dissipative Schr\"odinger…
We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…
We consider a loosely coupled, non-iterative Robin-Robin coupling method proposed and analyzed in [Numer. Algorithms, 99:921-948, 2025] for a parabolic-parabolic interface problem. We modify the first step of the scheme so that several…
Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators…