NDLI: Regularization Based on All-At-Once Formulations for Inverse Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Kaltenbacher, Barbara
Copyright Year	2016
Abstract	Parameter identification problems typically consist of a model equation, e.g., a (system of) ordinary or partial differential equation(s), and the observation equation. In the conventional reduced setting, the model equation is eliminated via the parameter-to-state map. Alternatively, one might consider both sets of equations (model and observations) as one large system, to which some regularization method is applied. The choice of the formulation (reduced or all-at-once) can make a large difference computationally, depending on which regularization method is used: Whereas almost the same optimality system arises for the reduced and the all-at-once Tikhonov method, the situation is different for iterative methods, especially in the context of nonlinear models. In this paper we will exemplarily provide some convergence results for all-at-once versions of variational, Newton type, and gradient based regularization methods. Moreover we will compare the implementation requirements for the respective all-at-once and reduced versions and provide some numerical comparison.
Sponsorship	Austrian Science Fund FWF. Alpen-Adria-Universitat Klagenfurt, Carinthian Economic Promotion Fund
Starting Page	2594
Ending Page	2618
Page Count	25
File Format	PDF
ISSN	00361429
DOI	10.1137/16M1060984
e-ISSN	10957170
Issue Number	4
Volume Number	54
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2016-08-30
Access Restriction	Subscribed
Subject Keyword	all-at-once formulations Inverse problems inverse problems regularization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in