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The theory of monotone operators plays a major role in modern optimization and many areas of nonlinera analysis. The central classes of monotone operators are matrices with a positive semidefinite symmetric part and subsifferential…

In order to solve Prandtl-type equations we propose a collocation-quadrature method based on VP filtered interpolation at Chebyshev nodes. Uniform convergence and stability are proved in a couple of Holder - Zygmund spaces of locally…

The need to approximate functions is ubiquitous in science, either due to empirical constraints or high computational cost of accessing the function. In high-energy physics, the precise computation of the scattering cross-section of a…

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…

The field of model order reduction (MOR) is growing in importance due to its ability to extract the key insights from complex simulations while discarding computationally burdensome and superfluous information. We provide an overview of MOR…

Interpolation for scattered data is a classical problem in numerical analysis, with a long history of theoretical and practical contributions. Recent advances have utilized deep neural networks to construct interpolators, exhibiting…

We prove sharp interpolatory estimates between Riesz Transforms and directional Haar projections. We obtain applications to the theory of compensated compactness and prove a conjecture of L. Tartar on semi-continuity of separately convex…

Nowadays, many fields of study are have to deal with large and sparse data matrixes, but the most important issue is finding the inverse of these matrixes. Thankfully, Krylov subspace methods can be used in solving these types of problem.…

When dealing with highly accurate modeling of time and frequency transfers into arbitrarily moving dielectrics medium, it may be convenient to work with Gordon's optical spacetime metric rather than the usual physical spacetime metric.…

Time delay estimation has long been an active area of research. In this work, we show that compressive sensing with interpolation may be used to achieve good estimation precision while lowering the sampling frequency. We propose an…

We investigate model order reduction (MOR) for linear dynamical systems, where a quadratic output is defined as a quantity of interest. The system can be transformed into a linear dynamical system with many linear outputs. MOR is feasible…

A method for data-driven interpolatory model reduction is presented in this extended abstract. This framework enables the computation of the transfer function values at given interpolation points based on time-domain input-output data only,…

In time-limited model order reduction, a reduced-order approximation of the original high-order model is obtained that accurately approximates the original model within the desired limited time interval. Accuracy outside that time interval…

We detail how to use Newton's method for distortion-based curved $r$-adaption to a discrete high-order metric field while matching a target geometry. Specifically, we combine two terms: a distortion measuring the deviation from the target…

The Realization Independent Iterative Rational Krylov Algorithm (TF-IRKA) is a frequency-based data-driven reduced order modeling (DDROM) method that constructs $\mathcal H_2$ optimal DDROMs. However, as the $\mathcal H_2$ optimal…

Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and…

We explore the properties of two-point cosmic propagators when Perturbation Theory (PT) loop corrections are consistently taken into account. We show in particular how the interpolation scheme proposed in arXiv:1112.3895 can be explicitly…

The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…

We study the problem of learning Markov decision processes with finite state and action spaces when the transition probability distributions and loss functions are chosen adversarially and are allowed to change with time. We introduce an…

This paper develops an interpolatory framework for weighted-$\mathcal{H}_2$ model reduction of MIMO dynamical systems. A new representation of the weighted-$\mathcal{H}_2$ inner products in MIMO settings is introduced and used to derive…