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Frozen Landweber Iteration for Nonlinear Ill-Posed Problems 被引量：8

Frozen Landweber Iteration for Nonlinear Ill-Posed Problems
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摘要 In this paper 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. In this paper 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.
作者 J.Xu B.Han L.Li
机构地区 Academy of Mathematics and Systems Science Department of Mathematics
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2007年第2期329-336,共8页 应用数学学报（英文版）
关键词 Ill-posed problem REGULARIZATION Landweber iteration Ill-posed problem, regularization, Landweber iteration
分类号 O177 [理学—基础数学]
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参考文献7

  • 1Engl, H.W., Hanke, M., Neubauer, A. Regularization of inverse problems. Kluwer, Dordrecht, 1996
  • 2Hanke, M. Accelerated Landweber iteration for the solution of ill-posed equations. Numer. Math., 60:341-373 (1991)
  • 3Hanke, M., Neubauer, A., Scherzer, O. A Convergence analysis of the Landweber iteration for nonlinearill-posed problems. Numer. Math., 72:21-37 (1995)
  • 4Neubauer, A. On Landweber iteration for nonlinear ill-posed problems in Hilbert scales. Numer. Math.,83:309-328 (2000)
  • 5Ramlau, R. A Modified Landweber method for inverse problems, Numer.Funct. Anal and Optimiz.,20(1): 7-98 (1999)
  • 6Scherzer, O. A Modified Landweber iteration for solving parameter estimation problems. Appl. Math.Optim., 38:45-68 (1998)
  • 7Samanskii, V. On a modification of the Newton method. (Russian) Ukrain. Mat. 2, 9:133-138 (1967)

同被引文献65

  • 1BI Chuanxing CHEN Xinzhao ZHOU Rong CHEN Jian.Landweber iterative regularization for nearfield acoustic holography[J].Chinese Science Bulletin,2006,51(11):1374-1380. 被引量：3
  • 2葛美宝,徐定华,王泽文,张文.一类抛物型方程反问题的数值解法[J].东华理工学院学报,2006,29(3):283-288. 被引量：7
  • 3Eriksson J, et al. Regularization methods for uniformly rankdeficient nonlinear least-squares problems [ J ]. Journal of Optimization Theory and Applications ,2005,127 (1) :1 -26.
  • 4Landweber L. An iteration formula for fredholm integral equations of the first kind amer [ J]. J. Math. , 1951,73 : 615 - 624.
  • 5Hanke M, Neubauer A and Scherzer O. A convergence analysis of the Landweber iteration for nonlinear ill-posed problems [ J ]. Numer. Math. , 1995,72:21 - 37.
  • 6Ku P gler. A derivative-free Landweber iteration for parameter identifiation in certain elliptic pdes [ J ]. Inverse Problems,2003,19 : 1 407 - 1 426.
  • 7ТихоновАН and АрсенинВЯ. Solutions of ill-posed problems [ M ]. New York : Wiley, 1977.
  • 8Eriksson J. Optimization and regularization of nonlinear leastsquares problems [ D ]. Umea University, Umea, Sweden, 1996.
  • 9王新洲.非线性模型线性近似的容许曲率[J].武汉测绘科技大学学报,1997,22(2):119-121. 被引量：13
  • 10LANDWEBER L. An iteration formula for fredholm integral equaions of the first kind [ J ]. American Journal Mathematics, 1951,73 (3) :615-624.

引证文献8

二级引证文献17

Acta Mathematicae Applicatae Sinica
2007年 第2期

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