Fractional Tikhonov regularization for linear discrete ill-posed problems

Tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least-squares problems with a severely ill-conditioned matrix A . This method replaces the given problem by a penalized least-squares problem. The present paper discusses measuring the residu...

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Bibliographic Details
Published in:	BIT (Nordisk Tidskrift for Informationsbehandling) Vol. 51; no. 1; pp. 197 - 215
Main Authors:	Hochstenbach, Michiel E., Reichel, Lothar
Format:	Journal Article Conference Proceeding
Language:	English
Published:	Dordrecht Springer Netherlands 01.03.2011 Springer
Subjects:	Algebra Algebraic geometry Computational Mathematics and Numerical Analysis Exact sciences and technology Mathematics Mathematics and Statistics Nonlinear algebraic and transcendental equations Numeric Computing Numerical analysis Numerical analysis in abstract spaces Numerical analysis. Scientific computation Numerical linear algebra Sciences and techniques of general use Weighted residual norm 65R30 Discrepancy principle 65F10 65F22 Filter function Solution norm constraint Fractional Tikhonov Ill-posed problem Regularization Error estimation Iterative method Tikhonov regularization Penalty method Non linear equation Direct method Linear equation Ill posed problem Transcendental equation Numerical linear algebra Least squares problem Pseudoinverse Equation system Regularization method Numerical analysis Linear system Matrix inversion overdetermined system Algebraic equation
ISSN:	0006-3835, 1572-9125
Online Access:	Get full text
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