A convergence analysis of the exponential Euler iteration for nonlinear ill-posed problems

Inverse Problems

Volumn 25, Issue 7, 2009, Pages

  Hochbruck, Marlis ^a   Hönig, Michael ^a   Ostermann, Alexander ^b  

^a HEINRICH HEINE UNIVERSITY   (Germany)

^b UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS ANALYSIS; CONVERGENCE ANALYSIS; DISCREPANCY PRINCIPLE; EULER METHOD; EXACT SOLUTION; JACOBIANS; LINEAR PROBLEMS; NONLINEAR ILL-POSED PROBLEMS; OPTIMAL CONVERGENCE; VARIABLE STEP SIZE;

DIFFERENTIAL EQUATIONS;

EID: 70350657165     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/25/7/075009     Document Type: Article

References (15)

1. Bakushinsky A B and Kokurin M Yu 2004 Iterative Methods for Approximate Solution of Inverse Problems (Dordrecht: Springer)
2. Dunford N and Schwartz J T 1988 Linear Operators. Part I: General Theory (New York: Wiley) (reprint of the 1958 original)
3. Hanke M 1997 A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems Inverse Problems 13 79-95
4. Hanke M 1997 Regularizing properties of a truncated Newton-cg algorithm for nonlinear inverse problems Numer. Funct. Anal. Optim. 18 971-93
5. Hanke M, Neubauer A and Scherzer O 1995 A convergence analysis of the Landweber iteration for nonlinear ill-posed problems Numer. Math. 72 21-37
6. Hochbruck M and Hönig M 2009 On the convergence of a regularizing Levenberg-Marquardt scheme for nonlinear ill-posed problems Technical Report Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Germany
7. Hochbruck M, Hönig M and Ostermann A Regularization of nonlinear ill-posed problems by exponential integrators Math. Modelling Numer. Anal. at press
8. Hochbruck M, Ostermann A and Schweitzer J 2009 Exponential Rosenbrock-type methods SIAM J. Numer. Anal. 47 786-803
9. Jin Q 2009 On a regularized Levenberg-Marquardt method for solving nonlinear inverse problems Technical Report University of Texas at Austin
10. Jin Q and Tautenhahn U 2009 On the discrepancy principles for some Newton type methods for solving nonlinear inverse problems Numer. Math. 111 509-58
11. Kaltenbacher B, Neubauer A and Scherzer O 2008 Iterative Regularization Methods for Nonlinear Ill-Posed Problems (New York: De Gruyter)
12. Rieder A 1999 On the regularization of nonlinear ill-posed problems via inexact Newton iterations Inverse Problems 15 309-27
13. Rieder A 2001 On convergence rates of inexact Newton regularizations Numer. Math. 88 347-65 (Pubitemid 33577009)
14. Showalter D 1967 Representation and computation of the pseudoinverse Proc. Am. Math. Soc. 18 584-6
15. Tautenhahn U 1994 On the asymptotical regularization of nonlinear ill-posed problems Inverse Problems 10 1405-18