×

zbMATH — the first resource for mathematics

Xu, J.; Han, B.; Li, L.
Frozen Landweber iteration for nonlinear ill-posed problems. (English) Zbl 1182.65085
Acta Math. Appl. Sin., Engl. Ser. 23, No. 2, 329-336 (2007).
Summary: We propose a modification of the Landweber iteration termed frozen Landweber iteration for nonlinear ill-posed problems. A convergence analysis for this iteration is presented. The numerical performance of this frozen Landweber iteration for a nonlinear Hammerstein integral equation is compared with that of the Landweber iteration. We obtain a shorter running time of the frozen Landweber iteration based on the same convergence accuracy.

Cited in 2 Documents
MSC:
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
47J06 Nonlinear ill-posed problems
45G10 Other nonlinear integral equations
65R20 Numerical methods for integral equations
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
Keywords:
regularization; Landweber iteration; numerical examples; nonlinear ill-posed problems; convergence; performance; nonlinear Hammerstein integral equation
PDF BibTeX XML Cite
\textit{J. Xu} et al., Acta Math. Appl. Sin., Engl. Ser. 23, No. 2, 329--336 (2007; Zbl 1182.65085)
Full Text: DOI
References:
[1] Engl, H.W., Hanke, M., Neubauer, A. Regularization of inverse problems. Kluwer, Dordrecht, 1996 · Zbl 0859.65054
[2] Hanke, M. Accelerated Landweber iteration for the solution of ill-posed equations. Numer. Math., 60: 341–373 (1991) · Zbl 0745.65038 · doi:10.1007/BF01385727
[3] Hanke, M., Neubauer, A., Scherzer, O. A Convergence analysis of the Landweber iteration for nonlinear ill-posed problems. Numer. Math., 72: 21–37 (1995) · Zbl 0840.65049 · doi:10.1007/s002110050158
[4] Neubauer, A. On Landweber iteration for nonlinear ill-posed problems in Hilbert scales. Numer. Math., 83: 309–328 (2000) · Zbl 0963.65058 · doi:10.1007/s002110050487
[5] Ramlau, R. A Modified Landweber method for inverse problems, Numer. Funct. Anal. and Optimiz., 20(1): 79–98 (1999) · Zbl 0970.65064 · doi:10.1080/01630569908816882
[6] Scherzer, O. A Modified Landweber iteration for solving parameter estimation problems. Appl. Math. Optim., 38: 45–68 (1998) · Zbl 0915.65054 · doi:10.1007/s002459900081
[7] Šamanskii, V. On a modification of the Newton method. (Russian) Ukrain. Mat. Ž, 9: 133–138 (1967)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.