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A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit…
One of the main difficulties in micromagnetics simulation is the norm preserving constraints $\|\mathbf{m}\|=1$ at the continuous or the discrete level. Another difficulty is the stability with the time step constraint. Using standard…
Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…
Iterative sketching and sketch-and-precondition are well-established randomized algorithms for solving large-scale, over-determined linear least-squares problems. In this paper, we introduce a new perspective that interprets Iterative…
The problem of robustly reconstructing a large number from its erroneous remainders with respect to several moduli, namely the robust remaindering problem, may occur in many applications including phase unwrapping, frequency detection from…
In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and…
We consider a reconstruction problem of a reduced stable positive network system with the preservation of the original interconnection structure based on an $H^2$ optimal model reduction problem with constraints. To this end, we define an…
Markov decisions processes (MDPs) are becoming increasing popular as models of decision theoretic planning. While traditional dynamic programming methods perform well for problems with small state spaces, structured methods are needed for…
In this paper we present a rigorous derivation of the reduced MHD models with and without parallel velocity that are implemented in the non-linear MHD code JOREK. The model we obtain contains some terms that have been neglected in the…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
A critical challenge inherent to the projection method applied to the Landau-Lifshitz equation is the deficiency of rigorous theoretical justifications for the stability of its projection step. To mitigate this limitation, we introduce a…
This paper mainly considers three iterations based on charge-conservative finite element approximation in Lipschitz domain for the stationary thermally coupled inductionless MHD equations. Based on the hybrid finite element method, the…
Transformer-based table retrieval systems flatten structured tables into token sequences, making retrieval sensitive to the choice of serialization even when table semantics remain unchanged. We show that semantically equivalent…
Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…
We study persistence modules defined on commutative ladders. This class of persistence modules frequently appears in topological data analysis, and the theory and algorithm proposed in this paper can be applied to these practical problems.…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
Solving inverse problems requires appropriate regularization techniques to ensure well-posedness and stability. In recent years, denoiser-driven methods have emerged as effective regularization strategies, achieving state-of-the-art…
In this paper, we study a numerical method for the solution of partial differential equations on evolving surfaces. The numerical method is built on the stabilized trace finite element method (TraceFEM) for the spatial discretization and…
Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps. RNNs have excellent expressive power but lack the stability or robustness guarantees that are necessary for many…
In this paper, an anti-eavesdropping estimation problem is investigated. A linear encryption scheme is utilized, which first linearly transforms innovation via an encryption matrix and then encrypts some components of the transformed…