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We present in this paper a novel numerical reconstruction method for solving a 3D coefficient inverse problem with scattering data generated by a single direction of the incident plane wave. This inverse problem is well-known to be a highly…

Numerical Analysis · Mathematics 2018-05-22 Michael V. Klibanov , Aleksandr E. Kolesov , Dinh-Liem Nguyen

We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary…

Analysis of PDEs · Mathematics 2020-01-08 Yavar Kian , Masahiro Yamamoto

In this paper, we develop a numerical algorithm for an inverse problem on determining fractional orders of time derivatives simultaneously in a coupled subdiffusion system. Following the theoretical uniqueness, we reformulate the order…

Numerical Analysis · Mathematics 2025-08-19 Yikan Liu

We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate…

Numerical Analysis · Mathematics 2017-12-21 Larisa Beilina , Kati Niinimäki

This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by…

Analysis of PDEs · Mathematics 2015-05-14 Guillaume Bal , Gunther Uhlmann

We discuss a Lagrangian reconstruction method of the velocity field from galaxy redshift catalog that takes its root in the Euler equation. This results in a ``functional'' of the velocity field which must be minimized. This is helped by an…

Astrophysics · Physics 2009-06-23 G. Lavaux

A simple flux reconstruction for finite element solutions of reaction-diffusion problems is shown to yield fully computable upper bounds on the energy norm of error in an approximation of singularly perturbed reaction-diffusion problem. The…

Numerical Analysis · Mathematics 2019-06-26 Mark Ainsworth , Tomas Vejchodsky

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…

Optimization and Control · Mathematics 2013-02-14 Ion Necoara , Andrei Patrascu

In this work we analyze the inverse problem of recovering the space-dependent potential coefficient in an elliptic / parabolic problem from distributed observation. We establish novel (weighted) conditional stability estimates under very…

Numerical Analysis · Mathematics 2022-12-21 Bangti Jin , Xiliang Lu , Qimeng Quan , Zhi Zhou

A problem of reconstruction of the topology and the respective edge resistance values of an unknown circular planar passive resistive network using limitedly available resistance distance measurements is considered. We develop a multistage…

Systems and Control · Electrical Eng. & Systems 2026-04-29 Shivanagouda Biradar , Deepak U Patil

In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigorous numerical analysis of the procedure. By exploiting…

Numerical Analysis · Mathematics 2024-05-20 Bangti Jin , Xiliang Lu , Qimeng Quan , Zhi Zhou

In this work, we consider the numerical recovery of a spatially dependent diffusion coefficient in a subdiffusion model from distributed observations. The subdiffusion model involves a Caputo fractional derivative of order $\alpha\in(0,1)$…

Numerical Analysis · Mathematics 2021-01-12 Bangti Jin , Zhi Zhou

Conductivity reconstruction in an inverse eddy current problem is considered in the present paper. With the electric field measurement on part of domain boundary, we formulate the reconstruction problem to a constrained optimization problem…

Numerical Analysis · Mathematics 2023-07-04 Junqing Chen , Zehao Long

In this paper, we present the analytical and numerical study of the optimization approach for determining the space-dependent source function in the parabolic inverse source problem using partial boundary measurements. The Lagrangian…

Numerical Analysis · Mathematics 2025-04-23 T. Sharma , L. Beilina , K. Sakthivel

We present a new stabilization technique for multiscale convection diffusion problems. Stabilization for these problems has been a challenging task, especially for the case with high Peclet numbers. Our method is based on a constraint…

Numerical Analysis · Mathematics 2018-08-01 Eric T. Chung , Yalchin Efendiev , Wing Tat Leung

The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this method are mainly derived for Lipschitz continuous objective functions. In this…

Optimization and Control · Mathematics 2024-11-01 Xiao Li , Lei Zhao , Daoli Zhu , Anthony Man-Cho So

We generalize and analyse the method for computing lower bounds of the principal eigenvalue proposed in our previous paper (I. Sebestova, T. Vejchodsky, SIAM J. Numer. Anal. 2014). This method is suitable for symmetric elliptic eigenvalue…

Numerical Analysis · Mathematics 2016-06-07 Ivana Sebestova , Tomas Vejchodsky

We consider the problem of recovering a real-valued $n$-dimensional signal from $m$ phaseless, linear measurements and analyze the amplitude-based non-smooth least squares objective. We establish local convergence of subgradient descent…

Machine Learning · Computer Science 2021-08-31 Paul Hand , Oscar Leong , Vladislav Voroninski

We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking…

Optimization and Control · Mathematics 2020-12-02 Julien Fageot , Matthieu Simeoni

We study the problem of minimizing the sum of potentially non-differentiable convex cost functions with partially overlapping dependences in an asynchronous manner, where communication in the network is not coordinated. We study the…

Optimization and Control · Mathematics 2021-02-17 Yankai Lin , Iman Shames , Dragan Nesic