Related papers: Comparative work for the source identification in …
Inverse Problem techniques offer powerful tools which deal naturally with marginal data and asymmetric or strongly smoothing kernels, in cases where parameter-fitting methods may be used only with some caution. Although they are typically…
In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization,…
Landweber-type methods are prominent for solving ill-posed inverse problems in Banach spaces and their convergence has been well-understood. However, how to derive their convergence rates remains a challenging open question. In this paper,…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
This paper investigates the inverse problems of determining a space-dependent source for thermoelastic systems of type III under adequate time-averaged or final-in-time measurements and conditions on the time-dependent part of the sought…
We propose a numerical method to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data. This problem arises in thermo- and photo- acoustic tomography in a bounded…
We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point…
We establish quantitative global stability estimates, formulated in terms of optimal transport (OT) cost, for inverse point-source problems governed by elliptic and parabolic equations with spatially varying coefficients. The key idea is…
A system of high-order adaptive multiresolution wavelet collocation upwind schemes are developed for the solution of hyperbolic conservation laws. A couple of asymmetrical wavelet bases with interpolation property are built to realize the…
The topics of source seeking and Newton-based extremum seeking have flourished, independently, but never combined. We present the first Newton-based source seeking algorithm. The algorithm employs forward velocity tuning, as in the very…
This paper investigates the solution of a parabolic inverse problem based upon the convection-diffusion-reaction equation, which can be used to estimate both water and air pollution. We will consider both known and unknown source location:…
Chebyshev spectral methods are widely used in numerical computations. When the underlying function has a singularity, it has been observed by L. N. Trefethen in 2011 that its Chebyshev interpolants exhibit an error localization property,…
We address the nonlinear inverse source problem of identifying a time-dependent source occurring in one node of a network governed by a wave equation. We prove that time records of the associated state taken at a strategic set of two nodes…
Wavelet-related techniques have proven useful in the processing and analysis of one and two dimensional data sets (spectra in the former case, images in the latter). In this work we apply adaptive filters, introduced in a previous work…
Source conditions of the type $x^\dag \in\mathcal{R}((A^\ast A)^\mu)$ are an important tool in the theory of inverse problems to show convergence rates of regularized solutions as the noise in the data goes to zero. Unfortunately, it is…
The objective of the present paper is to introduce the concept of a spatially inhomogeneous linear inverse problem where the degree of ill-posedness of operator $Q$ depends not only on the scale but also on location. In this case, the rates…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
The complexity of adaptive control of nonlinear time-varying systems requires the use of novel methods that have lower computational complexity as well as ensuring good performance under time-varying parameter changes. In this study, we use…
We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic…
In this paper, we study two types of inverse problems for space semi-discrete stochastic parabolic equations in arbitrary dimensions. The first problem concerns a semi-discrete inverse source problem, which involves determining the random…