Embedded techniques for choosing the parameter in Tikhonov regularization. Issue 6 (3rd April 2014)

• Record Type: Journal Article
• Authors: Gazzola, S.; Novati, P.; Russo, M. R.
• Is Part Of: Numerical linear algebra with applications. Volume 21:Issue 6(2014:Nov.)
• Page Start: 796
• Page End: 812
• Publication Date: 2014-04-03
• Subjects: Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.1934
• Languages: English
• ISSNs: 1070-5325

Abstract

<abstract abstract-type="main" id="nla1934-abs-0001"> <title>SUMMARY</title> <p id="nla1934-para-0001">This paper introduces a new strategy for setting the regularization parameter when solving large‐scale discrete ill‐posed linear problems by means of the Arnoldi–Tikhonov method. This new rule is essentially based on the discrepancy principle, although no initial knowledge of the norm of the error that affects the right‐hand side is assumed; an increasingly more accurate approximation of this quantity is recovered during the Arnoldi algorithm. Some theoretical estimates are derived in order to motivate our approach. Many numerical experiments performed on classical test problems as well as image deblurring problems are presented. Copyright © 2014 John Wiley &amp; Sons, Ltd.</p> </abstract>