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Strang splitting is a well established tool for the numerical integration of evolution equations. It allows the application of tailored integrators for different parts of the vector field. However, it is also prone to order reduction in the…

Numerical Analysis · Mathematics 2018-08-14 Lukas Einkemmer , Martina Moccaldi , Alexander Ostermann

In this article, stability estimates are given for the determination of the zeroth-order bounded perturbations of the biharmonic operator when the boundary Neumann measurements are made on the whole boundary and on slightly more than half…

Analysis of PDEs · Mathematics 2015-06-03 Anupam Pal Choudhury , Venkateswaran P. Krishnan

We consider a Strang-type second order operator-splitting discretization for the Cahn-Hilliard equation. We introduce a new theoretical framework and prove uniform energy stability of the numerical solution and persistence of all higher…

Numerical Analysis · Mathematics 2021-07-13 Dong Li , Chaoyu Quan

A backward stable numerical calculation of a function with condition number $\kappa$ will have a relative accuracy of $\kappa\epsilon_{\text{machine}}$. Standard formulations and software implementations of finite-strain elastic materials…

Numerical Analysis · Mathematics 2024-07-09 Rezgar Shakeri , Leila Ghaffari , Jeremy L. Thompson , Jed Brown

We perform a smoothed analysis of the componentwise condition numbers for determinant computation, matrix inversion, and linear equations solving for sparse n times n matrices. The bounds we obtain for the ex- pectations of the logarithm of…

Numerical Analysis · Mathematics 2013-02-26 Dennis Cheung , Felipe Cucker

We prove energy stability of a standard operator-splitting method for the Cahn-Hilliard equation. We establish uniform bound of Sobolev norms of the numerical solution and convergence of the splitting approximation. This is the first…

Numerical Analysis · Mathematics 2021-07-06 Dong Li , Chaoyu Quan

This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of…

Functional Analysis · Mathematics 2025-12-16 M. H. M. Rashid

In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…

Functional Analysis · Mathematics 2007-05-23 Paolo Dall'Aglio

For the inclusion problem involving two maximal monotone operators, under the metric subregularity of the composite operator, we derive the linear convergence of the generalized proximal point algorithm and several splitting algorithms,…

Optimization and Control · Mathematics 2016-09-28 Li Shen , Shaohua Pan

This note studies monotone Markov chains, a subclass of Markov chains with extensive applications in operations research and economics. While the properties that ensure the global stability of these chains are well studied, their…

Probability · Mathematics 2024-09-20 Bar Light

By applying some techniques of set-valued and variational analysis, we study solution stability of nonhomogeneous split equality problems and nonhomogeneous split feasibility problems, where the constraint sets need not be convex. Necessary…

Optimization and Control · Mathematics 2024-11-19 Vu Thi Huong , Hong-Kun Xu , Nguyen Dong Yen

Consensus control of multiagent systems arises in various robotic applications such as rendezvous and formation control. For example, to compute the control inputs of individual agents, the difference in the positions in aligned coordinate…

Systems and Control · Electrical Eng. & Systems 2024-10-22 Zhonggang Li , Changheng Li , Raj Thilak Rajan

We consider a general relation between fixed point stability of suitably perturbed transfer operators and convergence to equilibrium (a notion which is strictly related to decay of correlations). We apply this relation to deterministic…

Dynamical Systems · Mathematics 2018-03-28 Stefano Galatolo

We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…

Quantum Physics · Physics 2018-06-12 Vinay Tripathi , Chandrashekar Radhakrishnan , Tim Byrnes

We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular…

Analysis of PDEs · Mathematics 2014-03-27 Mauro Garavello , Rinaldo M. Colombo

We investigate errors in tangents and adjoints of implicit functions resulting from errors in the primal solution due to approximations computed by a numerical solver. Adjoints of systems of linear equations turn out to be unconditionally…

Numerical Analysis · Mathematics 2021-09-06 Uwe Naumann

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.

Functional Analysis · Mathematics 2010-11-23 J. Martin Lindsay , Kalyan B. Sinha

Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…

Systems and Control · Computer Science 2016-05-13 Matthias Lorenzen , Fabrizio Dabbene , Roberto Tempo , Frank Allgöwer

We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components which describe the coupling and the dynamics in the bulk and on the surface,…

Numerical Analysis · Mathematics 2022-10-19 Petra Csomós , Bálint Farkas , Balázs Kovács

This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…

Probability · Mathematics 2010-01-14 Manuel S. Santos