GKB-FP: An algorithm for large-scale discrete ill-posed problems. The authors present a new algorithm for discrete ill-posed problems, which is called GKB-FP. This method exploits the Golub-Kahan bidiagonalization algorithm together with Tikhonov regularization in the generated Krylov subspace. The regularization parameter for the projected problem is chosen by the fixed-point method already presented by the first author. A detailed convergence analysis is provided. The paper is enriched by many numerical results on well-known problems so that the effectiveness of the method appears comparable with other methods already used, and even better.

References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Jia, Zhongxiao: Approximation accuracy of the Krylov subspaces for linear discrete ill-posed problems (2020)
  2. Jozi, Meisam; Karimi, Saeed; Salkuyeh, Davod Khojasteh: An iterative method to compute minimum norm solutions of ill-posed problems in Hilbert spaces (2019)
  3. Karimi, Saeed; Jozi, Meisam: Weighted conjugate gradient-type methods for solving quadrature discretization of Fredholm integral equations of the first kind (2019)
  4. Bazán, Fermín S. V.; Bedin, Luciano; Borges, Leonardo S.: Space-dependent perfusion coefficient estimation in a 2D bioheat transfer problem (2017)
  5. Chung, Julianne; Saibaba, Arvind K.: Generalized hybrid iterative methods for large-scale Bayesian inverse problems (2017)
  6. Huang, Yi; Jia, ZhongXiao: Some results on the regularization of LSQR for large-scale discrete ill-posed problems (2017)
  7. Bazán, Fermín S. V.; Kleefeld, Andreas; Leem, Koung Hee; Pelekanos, George: Sampling method based projection approach for the reconstruction of 3D acoustically penetrable scatterers (2016)
  8. Chung, Julianne; Palmer, Katrina: A hybrid LSMR algorithm for large-scale Tikhonov regularization (2015)
  9. Viloche Bazán, Fermín S.: Simple and efficient determination of the Tikhonov regularization parameter chosen by the generalized discrepancy principle for discrete ill-posed problems (2015)
  10. Huang, Jie; Huang, Ting-Zhu; Zhao, Xi-Le; Xu, Zong-Ben; Lv, Xiao-Guang: Two soft-thresholding based iterative algorithms for image deblurring (2014) ioport
  11. Pavani, R.; Caliò, F.: About an artificial time approach for iterative numerical solution of Fredholm integral equations of the first kind (2014)
  12. Viloche Bazán, Fermín S.; Cunha, Maria C. C.; Borges, Leonardo S.: Extension of GKB-FP algorithm to large-scale general-form Tikhonov regularization. (2014)
  13. Viloche Bazán, Fermín S.; Borges, Leonardo S.; Francisco, Juliano B.: On a generalization of Regińska’s parameter choice rule and its numerical realization in large-scale multi-parameter Tikhonov regularization (2012)
  14. Viloche Bazán, Fermín S.; Borges, Leonardo S.: GKB-FP: An algorithm for large-scale discrete ill-posed problems (2010)