Estimation of the \(L\)-curve via Lanczos bidiagonalization
type: Item
instance of: scholarly article
title: Estimation of the \(L\)-curve via Lanczos bidiagonalization
zbMATH Open document ID: 0945.65044
DOI: 10.1023/A:1022383005969
author: Gene H. Golub
author: Daniela Calvetti
author: Lothar Reichel
published in: BIT
publication date: 2000-10-05T00:00:00Z
review text: A new approach is proposed to determine a value of the regularization parameter in solving ill-conditioned systems of linear equations with a right-hand side contamined by errors of unknown norm. The approach is based on computing an \(L\)-ribbon that contains the \(L\)-curve in its interior. An \(L\)-ribbon can be computed inexpensively by partial Lanczos bidiagonalization of the matrix of the given system of equations. A suitable value of the regularization parameter is then determined from the \(L\)-ribbon, and it is shown that an associated approximate solution of the linear system can be computed with little additional work.
Mathematics Subject Classification ID: 65F22
zbMATH DE Number: 1398423
zbMATH Keywords: regularization
zbMATH Keywords: ill-conditioned systems of linear equations
zbMATH Keywords: \(L\)-curve
zbMATH Keywords: partial Lanczos bidiagonalization
zbMATH Keywords: \(L\)-ribbon
reviewed by: Petko Hr. Petkov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1398423