GKB-FP swMATH ID: 2082 Software Authors: Viloche Bazán, Fermín S.; Borges, Leonardo S. Description: 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. Homepage: http://www.mtm.ufsc.br/~fermin/lancfp_rev.pdf Keywords: Tikhonov regularization; large-scale problems; discrete ill-posed problems; Golub-Kahan bidiagonalization; Krylov subspace; fixed-point method; convergence; numerical results Related Software: Regularization tools; LSQR; CRAIG; RestoreTools; LSMR; UTV; HyBR; IR Tools; AIR tools; Matlab; ForWaRD; NeNMF; ODL; GitHub; TIGRE; TomoPy; hIPPYlib; Parallel Colt; ASTRA; CCPi-Regularisation Cited in: 17 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year GKB-FP: An algorithm for large-scale discrete ill-posed problems. Zbl 1207.65039Viloche Bazán, Fermín S.; Borges, Leonardo S. 2010 all top 5 Cited by 25 Authors 7 Viloche Bazán, Fermín S. 5 Chung, Julianne M. 4 Borges, Leonardo Silveira 2 de Sturler, Eric 2 Jia, Zhongxiao 2 Jiang, Jiahua 2 Jozi, Meisam 2 Karimi, Saeed 1 Bedin, Luciano 1 Bozzoli, Fabio 1 Caliò, Franca 1 Cattani, Luca 1 Cunha, Maria Cristina C. 1 Francisco, Juliano B. 1 Gazzola, Silvia 1 Huang, Yi 1 Khojasteh Salkuyeh, Davod 1 Kleefeld, Andreas 1 Leem, Koung Hee 1 Mocerino, Andrea 1 Palmer, Katrina 1 Pavani, Raffaella 1 Pelekanos, George 1 Rainieri, Sara 1 Saibaba, Arvind Krishna all top 5 Cited in 14 Serials 4 SIAM Journal on Scientific Computing 1 Computer Physics Communications 1 Applied Mathematics and Computation 1 BIT 1 Journal of Computational and Applied Mathematics 1 Bulletin of the Iranian Mathematical Society 1 Journal of Scientific Computing 1 Linear Algebra and its Applications 1 SIAM Review 1 Numerical Linear Algebra with Applications 1 Far East Journal of Mathematical Sciences 1 Inverse Problems in Science and Engineering 1 Science China. Mathematics 1 Afrika Matematika all top 5 Cited in 11 Fields 17 Numerical analysis (65-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 3 Integral equations (45-XX) 2 Partial differential equations (35-XX) 2 Computer science (68-XX) 2 Information and communication theory, circuits (94-XX) 1 Operator theory (47-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX) Citations by Year