On $L^\infty$ stability for wave propagation and for linear inverse problems
METADATA ONLY
Loading...
Author / Producer
Date
2024-10-15
Publication Type
Working Paper
ETH Bibliography
yes
Citations
Altmetric
METADATA ONLY
Data
Rights / License
Abstract
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on energy conservation principles, and are therefore expressed in terms of $L^2$ norms. The focus of this paper is on stability with respect to the $L^\infty$ norm, which is more relevant to detect localized phenomena. The linear wave equation is not stable in $L^\infty$, and we design an alternative solution method based on the regularization of Fourier multipliers, which is stable in $L^\infty$. Furthermore, we show how these ideas can be extended to inverse problems, and design a regularization method for the inversion of compact operators that is stable in $L^\infty$. We also discuss the connection with the stability of deep neural networks modeled by hyperbolic PDEs.
Permanent link
Publication status
published
Editor
Book title
Journal / series
Volume
Pages / Article No.
2410.11467
Publisher
Cornell University
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Analysis of PDEs (math.AP); Numerical Analysis (math.NA); FOS: Mathematics; 35L05, 47A52, 65J20
Organisational unit
09603 - Alaifari, Rima (ehemalig) / Alaifari, Rima (former)