NDLI: A hybrid multilevel-active set method for large box-constrained linear discrete ill-posed problems

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CALCOLO : Volume 54

CALCOLO : Volume 53

CALCOLO : Volume 48, Issue 4, December 2011

CALCOLO : Volume 48, Issue 3, September 2011

CALCOLO : Volume 48, Issue 2, June 2011

CALCOLO : Volume 48, Issue 1, March 2011

Preface

Scattered data interpolation of Radon data

On kernel engineering via Paley–Wiener

On the application of the minimum polynomial extrapolation method to incompressible flows with heat transfer

Comparison of parameter choices in regularization algorithms in case of different information about noise level

A Smoothed Particle Image Reconstruction method

Numerical solution of the nonlinear Schrödinger equation, starting from the scattering data

A hybrid multilevel-active set method for large box-constrained linear discrete ill-posed problems

Curvature analysis of frequency modulated manifolds in dimensionality reduction

Data dependent weights in discontinuous weighted least-squares approximation with anisotropic support

A hybrid multilevel-active set method for large box-constrained linear discrete ill-posed problems

Content Provider	Springer Nature Link
Author	Reichel, L. Plemmons, R. Sgallari, F. Morigi, S.
Copyright Year	2010
Abstract	Many questions in science and engineering give rise to linear ill-posed problems, whose solution is known to satisfy box constraints, such as nonnegativity. The solution of discretized versions of these problems is highly sensitive to perturbations in the data, discretization errors, and round-off errors introduced during the computations. It is therefore often beneficial to impose known constraints during the solution process. This paper describes a two-phase algorithm for the solution of large-scale box-constrained linear discrete ill-posed problems. The first phase applies a cascadic multilevel method and imposes the constraints on each level by orthogonal projection. The second phase improves the computed approximate solution on the finest level by an active set method. The latter allows several indices of the active set to be updated simultaneously. This reduces the computational effort significantly, when compared to standard active set methods that update one index at a time. Applications to image restoration are presented.
Ending Page	105
Page Count	17
Starting Page	89
File Format	PDF
ISSN	00080624
e-ISSN	11265434
Journal	CALCOLO
Issue Number	1
Volume Number	48
Language	English
Publisher	Springer Milan
Publisher Date	2010-09-21
Publisher Place	Milan
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Optimization and variational techniques Multilevel method Iterative methods for linear systems Numerical Analysis Nonnegativity Theory of Computation Active set method Image restoration Improperly posed problems; regularization Constrained ill-posed problems
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory 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

Lavrentiev-type regularization methods for Hermitian problems

Numerical pseudodifferential operator and Fourier regularization

The Regularization Theory of the Krylov Iterative Solvers LSQR, CGLS, LSMR and CGME For Linear Discrete Ill-Posed Problems

Newton type iteration for Tikhonov regularization of non-linear ill-posed Hammerstein type equations

Comparison of parameter choices in regularization algorithms in case of different information about noise level

The regularization theory of the Krylov iterative solvers LSQR and CGLS for linear discrete ill-posed problems, part I: the simple singular value case

Estimation of the Regularization Parameter in Linear Discrete Ill-Posed Problems Using the Picard parameter

Approximation Accuracy of the Krylov Subspaces for Linear Discrete Ill-Posed Problems

An iterative regularization method for an abstract ill-posed biparabolic problem

A hybrid multilevel-active set method for large box-constrained linear discrete ill-posed problems

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