Related papers: Transfer function interpolation remainder formula …
Constructing a propagation map from a set of scattered measurements finds important applications in many areas, such as localization, spectrum monitoring and management. Classical interpolation-type methods have poor performance in regions…
The problem of computing Craig Interpolants has recently received a lot of interest. In this paper, we address the problem of efficient generation of interpolants for some important fragments of first order logic, which are amenable for…
We develop a constructive piecewise polynomial approximation theory in weighted Sobolev spaces with Muckenhoupt weights for any polynomial degree. The main ingredients to derive optimal error estimates for an averaged Taylor polynomial are…
Roundoff error problems have occurred frequently in interpolation methods of time-fractional equations, which can lead to undesirable results such as the failure of optimal convergence. These problems are essentially caused by catastrophic…
The paper addresses the model reduction problem for linear and nonlinear systems using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation…
In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or…
In this paper, we present an approach to enhance interpolation and approximation error estimates. Based on a previously derived first-order Taylor-like formula, we demonstrate its applicability in improving the $P_1$-interpolation error…
Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…
We present a modified model order reduction (MOR) technique for the FFT-based simulation of composite microstructures. It utilizes the earlier introduced MOR technique (Kochmann et al. [2019]), which is based on solving the…
Model order reduction (MOR) methods that are designed to preserve structural features of a given full order model (FOM) often suffer from a lower accuracy when compared to their non-structure-preserving counterparts. In this paper, we…
The constrained mock-Chebyshev least squares operator is a linear approximation operator based on an equispaced grid of points. Like other polynomial or rational approximation methods, it was recently introduced in order to defeat the Runge…
The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Nevertheless, there still exist challenging scenarios witnessing a…
We study the generalization error of functions that interpolate prescribed data points and are selected by minimizing a weighted norm. Under natural and general conditions, we prove that both the interpolants and their generalization errors…
Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…
The aim of this paper is to derive a refined first-order expansion formula in Rn, the goal being to get an optimal reduced remainder, compared to the one obtained by usual Taylor's formula. For a given function, the formula we derived is…
This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes with Incomplete Information and with semi-uniform Feller transition probabilities. The important…
We investigate the use of inexact solves for interpolatory model reduction and consider associated perturbation effects on the underlying model reduction problem. We give bounds on system perturbations induced by inexact solves and relate…
We present a registration procedure for parametric model order reduction (MOR) in two- and three-dimensional bounded domains. In the MOR framework, registration methods exploit solution snapshots to identify a parametric coordinate…
We consider transfer operators for topological Markov shift (TMS) with countable states and with holes which are $2$-cylinders. As main results, if the closed system of the shift has finitely irreducible transition matrix and the potential…
We study the phase transition phenomenon inherent in the shuffled (permuted) regression problem, which has found numerous applications in databases, privacy, data analysis, etc. In this study, we aim to precisely identify the locations of…