We study robustness properties of some iterative gradient-based methods for strongly convex functions, as well the larger class functions with sector-bounded gradients, under a relative error model. Proofs corresponding convergence rates are based on frequency-domain criteria stability nonlinear systems. Applications given to inexact versions gradient descent and Triple Momentum Method. To furt...

The determination of resolution parameter when estimating frequency functions of linear systems is a trade-off between bias and variance. Traditional approaches, like “window-closing” employ a global resolution parameter – the window width – that is tuned by ad hoc methods, usually visual inspection of the results. Here we explore more sophisticated estimation methods, based on local polynomial...

Abstract This expository paper is concerned with the direct integral formulations for boundary value problems of the Helmholtz equation. We discuss unique solvability for the corresponding boundary integral equations and its relations to the interior eigenvalue value problems of the Laplacian. Based on the integral representations, we study the asymptotic behaviors of the solutions to the bound...

For the detection of hidden objects by low-frequency electromagnetic imaging the Linear Sampling Method works remarkably well despite the fact that the rigorous mathematical justification is still incomplete. In this work, we give an explanation for this good performance by showing that in the low-frequency limit the measurement operator fulfills the assumptions for the fully justified variant ...