Onisk, Lucas; Reichel, Lothar; Sadok, Hassane Numerical considerations of block GMRES methods when applied to linear discrete ill-posed problems. (English) Zbl 1518.65038 J. Comput. Appl. Math. 430, Article ID 115262, 15 p. (2023). MSC: 65F22 PDFBibTeX XMLCite \textit{L. Onisk} et al., J. Comput. Appl. Math. 430, Article ID 115262, 15 p. (2023; Zbl 1518.65038) Full Text: DOI
Alkilayh, Maged; Reichel, Lothar Some numerical aspects of Arnoldi-Tikhonov regularization. (English) Zbl 1522.65055 Appl. Numer. Math. 185, 503-515 (2023). MSC: 65F22 65K05 PDFBibTeX XMLCite \textit{M. Alkilayh} and \textit{L. Reichel}, Appl. Numer. Math. 185, 503--515 (2023; Zbl 1522.65055) Full Text: DOI
Mohammady, Somaieh; Eslahchi, M. R. Application of fractional derivatives for obtaining new Tikhonov regularization matrices. (English) Zbl 1509.65032 J. Appl. Math. Comput. 69, No. 1, 1321-1342 (2023). MSC: 65F22 47A52 26A33 PDFBibTeX XMLCite \textit{S. Mohammady} and \textit{M. R. Eslahchi}, J. Appl. Math. Comput. 69, No. 1, 1321--1342 (2023; Zbl 1509.65032) Full Text: DOI
Alqahtani, A.; Mach, T.; Reichel, L. Solution of ill-posed problems with Chebfun. (English) Zbl 07669771 Numer. Algorithms 92, No. 4, 2341-2364 (2023). MSC: 65-XX 47A52 65F22 45B05 41A10 PDFBibTeX XMLCite \textit{A. Alqahtani} et al., Numer. Algorithms 92, No. 4, 2341--2364 (2023; Zbl 07669771) Full Text: DOI arXiv
Mach, T.; Reichel, L.; Van Barel, Marc Adaptive cross approximation for Tikhonov regularization in general form. (English) Zbl 1506.65247 Numer. Algorithms 92, No. 1, 815-830 (2023). MSC: 65R10 65F22 PDFBibTeX XMLCite \textit{T. Mach} et al., Numer. Algorithms 92, No. 1, 815--830 (2023; Zbl 1506.65247) Full Text: DOI arXiv
de Alba, Patricia Díaz; Fermo, Luisa; Pes, Federica; Rodriguez, Giuseppe Regularized minimal-norm solution of an overdetermined system of first kind integral equations. (English) Zbl 07644398 Numer. Algorithms 92, No. 1, 471-502 (2023). MSC: 65R30 65R32 45Q05 86A22 PDFBibTeX XMLCite \textit{P. D. de Alba} et al., Numer. Algorithms 92, No. 1, 471--502 (2023; Zbl 07644398) Full Text: DOI arXiv
Alqahtani, A.; Ramlau, R.; Reichel, L. Error estimates for Golub-Kahan bidiagonalization with Tikhonov regularization for ill-posed operator equations. (English) Zbl 07640669 Inverse Probl. 39, No. 2, Article ID 025002, 27 p. (2023). MSC: 47A52 35Rxx PDFBibTeX XMLCite \textit{A. Alqahtani} et al., Inverse Probl. 39, No. 2, Article ID 025002, 27 p. (2023; Zbl 07640669) Full Text: DOI
Shehu, Yekini; Vuong, Phan Tu; Zemkoho, Alain An inertial extrapolation method for convex simple bilevel optimization. (English) Zbl 1464.90101 Optim. Methods Softw. 36, No. 1, 1-19 (2021). MSC: 90C30 PDFBibTeX XMLCite \textit{Y. Shehu} et al., Optim. Methods Softw. 36, No. 1, 1--19 (2021; Zbl 1464.90101) Full Text: DOI arXiv
Mekoth, Chitra; George, Santhosh; Jidesh, P. Fractional Tikhonov regularization method in Hilbert scales. (English) Zbl 1474.47035 Appl. Math. Comput. 392, Article ID 125701, 26 p. (2021). MSC: 47A52 65R10 65J10 47H09 49J30 PDFBibTeX XMLCite \textit{C. Mekoth} et al., Appl. Math. Comput. 392, Article ID 125701, 26 p. (2021; Zbl 1474.47035) Full Text: DOI
Bai, Xianglan; Huang, Guang-Xin; Lei, Xiao-Jun; Reichel, Lothar; Yin, Feng A novel modified TRSVD method for large-scale linear discrete ill-posed problems. (English) Zbl 1460.65041 Appl. Numer. Math. 164, 72-88 (2021). MSC: 65F22 15A23 PDFBibTeX XMLCite \textit{X. Bai} et al., Appl. Numer. Math. 164, 72--88 (2021; Zbl 1460.65041) Full Text: DOI
Reichel, Lothar; Sadok, Hassane; Zhang, Wei-Hong Simple stopping criteria for the LSQR method applied to discrete ill-posed problems. (English) Zbl 1462.65040 Numer. Algorithms 84, No. 4, 1381-1395 (2020). MSC: 65F22 65F10 PDFBibTeX XMLCite \textit{L. Reichel} et al., Numer. Algorithms 84, No. 4, 1381--1395 (2020; Zbl 1462.65040) Full Text: DOI
Buccini, Alessandro; Pasha, Mirjeta; Reichel, Lothar Generalized singular value decomposition with iterated Tikhonov regularization. (English) Zbl 1524.65177 J. Comput. Appl. Math. 373, Article ID 112276, 9 p. (2020). MSC: 65F22 15A18 PDFBibTeX XMLCite \textit{A. Buccini} et al., J. Comput. Appl. Math. 373, Article ID 112276, 9 p. (2020; Zbl 1524.65177) Full Text: DOI Link
Buccini, Alessandro; Park, Yonggi; Reichel, Lothar Comparison of a-posteriori parameter choice rules for linear discrete ill-posed problems. (English) Zbl 1441.65045 J. Comput. Appl. Math. 373, Article ID 112138, 7 p. (2020); corrigendum ibid. 397, Article ID 113571, 1 p. (2021). Reviewer: Constantin Popa (Constanţa) MSC: 65F22 65F10 65R32 PDFBibTeX XMLCite \textit{A. Buccini} et al., J. Comput. Appl. Math. 373, Article ID 112138, 7 p. (2020; Zbl 1441.65045) Full Text: DOI Link
Mohammady, Somaieh; Eslahchi, M. R. Extension of Tikhonov regularization method using linear fractional programming. (English) Zbl 1441.47009 J. Comput. Appl. Math. 371, Article ID 112677, 16 p. (2020). Reviewer: Akhtar Khan (Rochester) MSC: 47A52 65F22 49K40 65N20 PDFBibTeX XMLCite \textit{S. Mohammady} and \textit{M. R. Eslahchi}, J. Comput. Appl. Math. 371, Article ID 112677, 16 p. (2020; Zbl 1441.47009) Full Text: DOI
Gazzola, Silvia; Noschese, Silvia; Novati, Paolo; Reichel, Lothar Arnoldi decomposition, GMRES, and preconditioning for linear discrete ill-posed problems. (English) Zbl 1417.65119 Appl. Numer. Math. 142, 102-121 (2019). MSC: 65F22 65F10 65F35 PDFBibTeX XMLCite \textit{S. Gazzola} et al., Appl. Numer. Math. 142, 102--121 (2019; Zbl 1417.65119) Full Text: DOI arXiv
Onunwor, Enyinda; Reichel, Lothar On the computation of a truncated SVD of a large linear discrete ill-posed problem. (English) Zbl 1368.65063 Numer. Algorithms 75, No. 2, 359-380 (2017). MSC: 65F20 65F22 PDFBibTeX XMLCite \textit{E. Onunwor} and \textit{L. Reichel}, Numer. Algorithms 75, No. 2, 359--380 (2017; Zbl 1368.65063) Full Text: DOI
Novati, Paolo Some properties of the Arnoldi-based methods for linear ill-posed problems. (English) Zbl 1367.65084 SIAM J. Numer. Anal. 55, No. 3, 1437-1455 (2017). MSC: 65J20 65J10 47A52 47B07 PDFBibTeX XMLCite \textit{P. Novati}, SIAM J. Numer. Anal. 55, No. 3, 1437--1455 (2017; Zbl 1367.65084) Full Text: DOI
Bentbib, A. H.; El Guide, M.; Jbilou, K.; Reichel, L. Global Golub-Kahan bidiagonalization applied to large discrete ill-posed problems. (English) Zbl 1365.65102 J. Comput. Appl. Math. 322, 46-56 (2017). MSC: 65F22 65F10 65R20 45B05 65R30 PDFBibTeX XMLCite \textit{A. H. Bentbib} et al., J. Comput. Appl. Math. 322, 46--56 (2017; Zbl 1365.65102) Full Text: DOI
Mach, T.; Reichel, L.; Van Barel, M.; Vandebril, R. Adaptive cross approximation for ill-posed problems. (English) Zbl 1416.65565 J. Comput. Appl. Math. 303, 206-217 (2016). MSC: 65R32 45Q05 65F50 65F15 PDFBibTeX XMLCite \textit{T. Mach} et al., J. Comput. Appl. Math. 303, 206--217 (2016; Zbl 1416.65565) Full Text: DOI
Hochstenbach, Michiel E.; Noschese, Silvia; Reichel, Lothar Fractional regularization matrices for linear discrete ill-posed problems. (English) Zbl 1360.65113 J. Eng. Math. 93, 113-129 (2015). MSC: 65F22 PDFBibTeX XMLCite \textit{M. E. Hochstenbach} et al., J. Eng. Math. 93, 113--129 (2015; Zbl 1360.65113) Full Text: DOI Link
Bouhamidi, A.; Jbilou, K.; Reichel, L.; Sadok, H.; Wang, Z. Vector extrapolation applied to truncated singular value decomposition and truncated iteration. (English) Zbl 1360.65109 J. Eng. Math. 93, 99-112 (2015). MSC: 65F15 PDFBibTeX XMLCite \textit{A. Bouhamidi} et al., J. Eng. Math. 93, 99--112 (2015; Zbl 1360.65109) Full Text: DOI
Reichel, Lothar; Yu, Xuebo Tikhonov regularization via flexible Arnoldi reduction. (English) Zbl 1332.65058 BIT 55, No. 4, 1145-1168 (2015). MSC: 65F22 65F10 PDFBibTeX XMLCite \textit{L. Reichel} and \textit{X. Yu}, BIT 55, No. 4, 1145--1168 (2015; Zbl 1332.65058) Full Text: DOI
Bellalij, M.; Reichel, L.; Sadok, H. Some properties of range restricted GMRES methods. (English) Zbl 1321.65046 J. Comput. Appl. Math. 290, 310-318 (2015). MSC: 65F10 65F22 PDFBibTeX XMLCite \textit{M. Bellalij} et al., J. Comput. Appl. Math. 290, 310--318 (2015; Zbl 1321.65046) Full Text: DOI
Hochstenbach, M. E.; Reichel, L.; Rodriguez, G. Regularization parameter determination for discrete ill-posed problems. (English) Zbl 1295.65046 J. Comput. Appl. Math. 273, 132-149 (2015). MSC: 65F22 65F20 PDFBibTeX XMLCite \textit{M. E. Hochstenbach} et al., J. Comput. Appl. Math. 273, 132--149 (2015; Zbl 1295.65046) Full Text: DOI
Donatelli, M.; Reichel, L. Square smoothing regularization matrices with accurate boundary conditions. (English) Zbl 1294.65099 J. Comput. Appl. Math. 272, 334-349 (2014). MSC: 65N20 65N06 35J25 65F22 PDFBibTeX XMLCite \textit{M. Donatelli} and \textit{L. Reichel}, J. Comput. Appl. Math. 272, 334--349 (2014; Zbl 1294.65099) Full Text: DOI
Morikuni, Keiichi; Reichel, Lothar; Hayami, Ken FGMRES for linear discrete ill-posed problems. (English) Zbl 1302.65081 Appl. Numer. Math. 75, 175-187 (2014). MSC: 65F10 65F08 65F22 PDFBibTeX XMLCite \textit{K. Morikuni} et al., Appl. Numer. Math. 75, 175--187 (2014; Zbl 1302.65081) Full Text: DOI
Donatelli, Marco; Neuman, Arthur; Reichel, Lothar Square regularization matrices for large linear discrete ill-posed problems. (English) Zbl 1289.65096 Numer. Linear Algebra Appl. 19, No. 6, 896-913 (2012). Reviewer: Fiorella Sgallari (Bologna) MSC: 65F22 65F10 65N06 65F20 PDFBibTeX XMLCite \textit{M. Donatelli} et al., Numer. Linear Algebra Appl. 19, No. 6, 896--913 (2012; Zbl 1289.65096) Full Text: DOI
Noschese, Silvia; Reichel, Lothar Inverse problems for regularization matrices. (English) Zbl 1254.65053 Numer. Algorithms 60, No. 4, 531-544 (2012). MSC: 65F22 PDFBibTeX XMLCite \textit{S. Noschese} and \textit{L. Reichel}, Numer. Algorithms 60, No. 4, 531--544 (2012; Zbl 1254.65053) Full Text: DOI
Reichel, Lothar; Sgallari, Fiorella; Ye, Qiang Tikhonov regularization based on generalized Krylov subspace methods. (English) Zbl 1246.65068 Appl. Numer. Math. 62, No. 9, 1215-1228 (2012). MSC: 65F22 PDFBibTeX XMLCite \textit{L. Reichel} et al., Appl. Numer. Math. 62, No. 9, 1215--1228 (2012; Zbl 1246.65068) Full Text: DOI
Neuman, A.; Reichel, L.; Sadok, H. Implementations of range restricted iterative methods for linear discrete ill-posed problems. (English) Zbl 1241.65045 Linear Algebra Appl. 436, No. 10, 3974-3990 (2012). MSC: 65F22 PDFBibTeX XMLCite \textit{A. Neuman} et al., Linear Algebra Appl. 436, No. 10, 3974--3990 (2012; Zbl 1241.65045) Full Text: DOI
Neuman, Arthur; Reichel, Lothar; Sadok, Hassane Algorithms for range restricted iterative methods for linear discrete ill-posed problems. (English) Zbl 1236.65040 Numer. Algorithms 59, No. 2, 325-331 (2012). MSC: 65F22 PDFBibTeX XMLCite \textit{A. Neuman} et al., Numer. Algorithms 59, No. 2, 325--331 (2012; Zbl 1236.65040) Full Text: DOI
Hochstenbach, Michiel E.; Reichel, Lothar An iterative method for Tikhonov regularization with a general linear regularization operator. (English) Zbl 1210.65092 J. Integral Equations Appl. 22, No. 3, 465-482 (2010). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F22 65R30 65F10 65F20 45B05 68U10 PDFBibTeX XMLCite \textit{M. E. Hochstenbach} and \textit{L. Reichel}, J. Integral Equations Appl. 22, No. 3, 465--482 (2010; Zbl 1210.65092) Full Text: DOI
Landi, G.; Loli Piccolomini, E. An iterative Lagrange method for the regularization of discrete ill-posed inverse problems. (English) Zbl 1202.65183 Comput. Math. Appl. 60, No. 6, 1723-1738 (2010). MSC: 65R30 PDFBibTeX XMLCite \textit{G. Landi} and \textit{E. Loli Piccolomini}, Comput. Math. Appl. 60, No. 6, 1723--1738 (2010; Zbl 1202.65183) Full Text: DOI
Hochstenbach, Michiel E.; Reichel, Lothar Subspace-restricted singular value decompositions for linear discrete ill-posed problems. (English) Zbl 1204.65038 J. Comput. Appl. Math. 235, No. 4, 1053-1064 (2010). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65F22 65F20 PDFBibTeX XMLCite \textit{M. E. Hochstenbach} and \textit{L. Reichel}, J. Comput. Appl. Math. 235, No. 4, 1053--1064 (2010; Zbl 1204.65038) Full Text: DOI
Morigi, S.; Reichel, L.; Sgallari, F. Noise-reducing cascadic multilevel methods for linear discrete ill-posed problems. (English) Zbl 1219.65042 Numer. Algorithms 53, No. 1, 1-22 (2010). MSC: 65F22 94A08 PDFBibTeX XMLCite \textit{S. Morigi} et al., Numer. Algorithms 53, No. 1, 1--22 (2010; Zbl 1219.65042) Full Text: DOI
Reichel, Lothar; Shyshkov, Andriy Cascadic multilevel methods for ill-posed problems. (English) Zbl 1186.65069 J. Comput. Appl. Math. 233, No. 5, 1314-1325 (2010). Reviewer: Robert Plato (Siegen) MSC: 65J10 65J20 47A52 PDFBibTeX XMLCite \textit{L. Reichel} and \textit{A. Shyshkov}, J. Comput. Appl. Math. 233, No. 5, 1314--1325 (2010; Zbl 1186.65069) Full Text: DOI
Reichel, L.; Rodriguez, G.; Seatzu, S. Error estimates for large-scale ill-posed problems. (English) Zbl 1166.65332 Numer. Algorithms 51, No. 3, 341-361 (2009). MSC: 65F22 PDFBibTeX XMLCite \textit{L. Reichel} et al., Numer. Algorithms 51, No. 3, 341--361 (2009; Zbl 1166.65332) Full Text: DOI
Jbilou, K.; Reichel, L.; Sadok, H. Vector extrapolation enhanced TSVD for linear discrete ill-posed problems. (English) Zbl 1167.65019 Numer. Algorithms 51, No. 2, 195-208 (2009). MSC: 65F20 65F22 PDFBibTeX XMLCite \textit{K. Jbilou} et al., Numer. Algorithms 51, No. 2, 195--208 (2009; Zbl 1167.65019) Full Text: DOI
Lewis, Bryan; Reichel, Lothar Arnoldi-Tikhonov regularization methods. (English) Zbl 1166.65016 J. Comput. Appl. Math. 226, No. 1, 92-102 (2009). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F22 65F10 PDFBibTeX XMLCite \textit{B. Lewis} and \textit{L. Reichel}, J. Comput. Appl. Math. 226, No. 1, 92--102 (2009; Zbl 1166.65016) Full Text: DOI
Reichel, L.; Ye, Q. A generalized LSQR algorithm. (English) Zbl 1212.65170 Numer. Linear Algebra Appl. 15, No. 7, 643-660 (2008). MSC: 65F22 65F10 65F20 PDFBibTeX XMLCite \textit{L. Reichel} and \textit{Q. Ye}, Numer. Linear Algebra Appl. 15, No. 7, 643--660 (2008; Zbl 1212.65170) Full Text: DOI
Reichel, Lothar; Shyshkov, Andriy A new zero-finder for Tikhonov regularization. (English) Zbl 1161.65029 BIT 48, No. 3, 627-643 (2008). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65F22 65F20 PDFBibTeX XMLCite \textit{L. Reichel} and \textit{A. Shyshkov}, BIT 48, No. 3, 627--643 (2008; Zbl 1161.65029) Full Text: DOI
Reichel, L.; Sadok, H.; Shyshkov, A. Greedy Tikhonov regularization for large linear ill-posed problems. (English) Zbl 1125.65034 Int. J. Comput. Math. 84, No. 8, 1151-1166 (2007). Reviewer: Iulian Coroian (Baia Mare) MSC: 65F22 65F10 65R30 45B05 PDFBibTeX XMLCite \textit{L. Reichel} et al., Int. J. Comput. Math. 84, No. 8, 1151--1166 (2007; Zbl 1125.65034) Full Text: DOI
Baglama, James; Reichel, Lothar Decomposition methods for large linear discrete ill-posed problems. (English) Zbl 1106.65035 J. Comput. Appl. Math. 198, No. 2, 332-343 (2007). Reviewer: Liu Xinguo (Qingdao) MSC: 65F22 65F10 PDFBibTeX XMLCite \textit{J. Baglama} and \textit{L. Reichel}, J. Comput. Appl. Math. 198, No. 2, 332--343 (2007; Zbl 1106.65035) Full Text: DOI
Calvetti, D.; Reichel, L.; Shuibi, A. Invertible smoothing preconditioners for linear discrete ill-posed problems. (English) Zbl 1072.65057 Appl. Numer. Math. 54, No. 2, 135-149 (2005). MSC: 65F22 65F35 PDFBibTeX XMLCite \textit{D. Calvetti} et al., Appl. Numer. Math. 54, No. 2, 135--149 (2005; Zbl 1072.65057) Full Text: DOI
Calvetti, D.; Reichel, L.; Shuibi, A. Enriched Krylov subspace methods for ill-posed problems. (English) Zbl 1017.65025 Linear Algebra Appl. 362, 257-273 (2003). Reviewer: Dietrich Braess (Bochum) MSC: 65F10 65F22 PDFBibTeX XMLCite \textit{D. Calvetti} et al., Linear Algebra Appl. 362, 257--273 (2003; Zbl 1017.65025) Full Text: DOI
Calvetti, D.; Morigi, S.; Reichel, L.; Sgallari, F. Tikhonov regularization and the L-curve for large discrete ill-posed problems. (English) Zbl 0977.65030 J. Comput. Appl. Math. 123, No. 1-2, 423-446 (2000). Reviewer: O.Vaarmann (Tallinn) MSC: 65F22 PDFBibTeX XMLCite \textit{D. Calvetti} et al., J. Comput. Appl. Math. 123, No. 1--2, 423--446 (2000; Zbl 0977.65030) Full Text: DOI
Baart, M. L.; McLeod, R. J. Y. Continuous quadric patch approximation of curved surfaces. (English) Zbl 0728.65012 Comput. Math. Appl. 22, No. 8, 11-20 (1991). MSC: 65D17 PDFBibTeX XMLCite \textit{M. L. Baart} and \textit{R. J. Y. McLeod}, Comput. Math. Appl. 22, No. 8, 11--20 (1991; Zbl 0728.65012) Full Text: DOI
Hansen, P. C. Computation of the singular value expansion. (English) Zbl 0631.65133 Computing 40, No. 3, 185-199 (1988). MSC: 65R20 45C05 PDFBibTeX XMLCite \textit{P. C. Hansen}, Computing 40, No. 3, 185--199 (1988; Zbl 0631.65133) Full Text: DOI
Lamoureux, M.; Wolkowicz, H. Numerical decomposition of a convex function. (English) Zbl 0548.90053 J. Optimization Theory Appl. 47, 51-64 (1985). MSC: 90C25 90C55 26B25 PDFBibTeX XMLCite \textit{M. Lamoureux} and \textit{H. Wolkowicz}, J. Optim. Theory Appl. 47, 51--64 (1985; Zbl 0548.90053) Full Text: DOI