Li, Haibo The joint bidiagonalization of a matrix pair with inaccurate inner iterations. (English) Zbl 07791526 SIAM J. Matrix Anal. Appl. 45, No. 1, 232-259 (2024). MSC: 65F25 65F20 15A18 65G99 PDFBibTeX XMLCite \textit{H. Li}, SIAM J. Matrix Anal. Appl. 45, No. 1, 232--259 (2024; Zbl 07791526) Full Text: DOI arXiv
Baglama, James; Perović, Vasilije Explicit deflation in Golub-Kahan-Lanczos bidiagonalization methods. (English) Zbl 1512.65059 ETNA, Electron. Trans. Numer. Anal. 58, 164-176 (2023). MSC: 65F15 65F50 15A18 PDFBibTeX XMLCite \textit{J. Baglama} and \textit{V. Perović}, ETNA, Electron. Trans. Numer. Anal. 58, 164--176 (2023; Zbl 1512.65059) Full Text: DOI Link
Jia, Zhongxiao; Li, Haibo The joint bidiagonalization method for large GSVD computations in finite precision. (English) Zbl 1516.65029 SIAM J. Matrix Anal. Appl. 44, No. 1, 382-407 (2023). MSC: 65F15 65F20 65F25 15A18 65F50 65G50 PDFBibTeX XMLCite \textit{Z. Jia} and \textit{H. Li}, SIAM J. Matrix Anal. Appl. 44, No. 1, 382--407 (2023; Zbl 1516.65029) Full Text: DOI arXiv
Baglama, James; Perović, Vasilije; Picucci, Jennifer Hybrid iterative refined restarted Lanczos bidiagonalization methods. (English) Zbl 1506.65060 Numer. Algorithms 92, No. 2, 1183-1212 (2023). MSC: 65F15 65F50 15A18 PDFBibTeX XMLCite \textit{J. Baglama} et al., Numer. Algorithms 92, No. 2, 1183--1212 (2023; Zbl 1506.65060) Full Text: DOI
Guo, Qiang; Zhang, Yongxia; Qiu, Shi; Zhang, Caiming Accelerating patch-based low-rank image restoration using kd-forest and Lanczos approximation. (English) Zbl 1484.68296 Inf. Sci. 556, 177-193 (2021). MSC: 68U10 65F55 PDFBibTeX XMLCite \textit{Q. Guo} et al., Inf. Sci. 556, 177--193 (2021; Zbl 1484.68296) Full Text: DOI
Jia, Zhongxiao; Li, Haibo The joint bidiagonalization process with partial reorthogonalization. (English) Zbl 1485.65038 Numer. Algorithms 88, No. 2, 965-992 (2021). MSC: 65F15 15A18 65F25 PDFBibTeX XMLCite \textit{Z. Jia} and \textit{H. Li}, Numer. Algorithms 88, No. 2, 965--992 (2021; Zbl 1485.65038) Full Text: DOI arXiv
Rezaiee-Pajand, Mohammad; Sarmadi, Hassan; Entezami, Alireza A hybrid sensitivity function and Lanczos bidiagonalization-Tikhonov method for structural model updating: application to a full-scale bridge structure. (English) Zbl 1481.74609 Appl. Math. Modelling 89, Part 1, 860-884 (2021). MSC: 74P10 65F15 PDFBibTeX XMLCite \textit{M. Rezaiee-Pajand} et al., Appl. Math. Modelling 89, Part 1, 860--884 (2021; Zbl 1481.74609) Full Text: DOI
Jia, Zhongxiao Approximation accuracy of the Krylov subspaces for linear discrete ill-posed problems. (English) Zbl 1434.65043 J. Comput. Appl. Math. 374, Article ID 112786, 25 p. (2020). Reviewer: Constantin Popa (Constanţa) MSC: 65F22 15A18 65F10 65F20 65R32 65J20 65J22 65R30 47A52 15A29 45Q05 86A22 PDFBibTeX XMLCite \textit{Z. Jia}, J. Comput. Appl. Math. 374, Article ID 112786, 25 p. (2020; Zbl 1434.65043) Full Text: DOI arXiv
Ohashi, A.; Sogabe, T. On computing the minimum singular value of a tensor sum. (English) Zbl 1433.65057 Spec. Matrices 7, 95-106 (2019). MSC: 65F15 15A69 65F20 PDFBibTeX XMLCite \textit{A. Ohashi} and \textit{T. Sogabe}, Spec. Matrices 7, 95--106 (2019; Zbl 1433.65057) Full Text: DOI
Caruso, Noe Angelo; Novati, Paolo Convergence analysis of LSQR for compact operator equations. (English) Zbl 1425.65048 Linear Algebra Appl. 583, 146-164 (2019). MSC: 65F10 65F22 65R32 PDFBibTeX XMLCite \textit{N. A. Caruso} and \textit{P. Novati}, Linear Algebra Appl. 583, 146--164 (2019; Zbl 1425.65048) Full Text: DOI
Jia, Zhigang; Ng, Michael K.; Song, Guang-Jing Lanczos method for large-scale quaternion singular value decomposition. (English) Zbl 07107363 Numer. Algorithms 82, No. 2, 699-717 (2019). MSC: 65-XX PDFBibTeX XMLCite \textit{Z. Jia} et al., Numer. Algorithms 82, No. 2, 699--717 (2019; Zbl 07107363) Full Text: DOI
Xie, Pengpeng; Xiang, Hua; Wei, Yimin Randomized algorithms for total least squares problems. (English) Zbl 1524.65181 Numer. Linear Algebra Appl. 26, No. 1, e2219, 16 p. (2019). MSC: 65F25 65F20 65K10 PDFBibTeX XMLCite \textit{P. Xie} et al., Numer. Linear Algebra Appl. 26, No. 1, e2219, 16 p. (2019; Zbl 1524.65181) Full Text: DOI
Novati, P. A convergence result for some Krylov-Tikhonov methods in Hilbert spaces. (English) Zbl 1392.65068 Numer. Funct. Anal. Optim. 39, No. 6, 655-666 (2018). MSC: 65F10 65F22 65R32 PDFBibTeX XMLCite \textit{P. Novati}, Numer. Funct. Anal. Optim. 39, No. 6, 655--666 (2018; Zbl 1392.65068) Full Text: DOI
Xu, Hong-Xiu Zhong Hongguo Weighted Golub-Kahan-Lanczos bidiagonalization algorithms. (English) Zbl 1392.65101 ETNA, Electron. Trans. Numer. Anal. 47, 153-178 (2017). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{H.-X. Z. H. Xu}, ETNA, Electron. Trans. Numer. Anal. 47, 153--178 (2017; Zbl 1392.65101) Full Text: Link
Huang, Yi; Jia, ZhongXiao Some results on the regularization of LSQR for large-scale discrete ill-posed problems. (English) Zbl 1453.65080 Sci. China, Math. 60, No. 4, 701-718 (2017). Reviewer: Constantin Popa (Constanţa) MSC: 65F22 65J20 15A18 PDFBibTeX XMLCite \textit{Y. Huang} and \textit{Z. Jia}, Sci. China, Math. 60, No. 4, 701--718 (2017; Zbl 1453.65080) 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
Gaaf, Sarah W.; Simoncini, Valeria Approximating the leading singular triplets of a large matrix function. (English) Zbl 1355.65062 Appl. Numer. Math. 113, 26-43 (2017). MSC: 65F60 15A18 65F20 PDFBibTeX XMLCite \textit{S. W. Gaaf} and \textit{V. Simoncini}, Appl. Numer. Math. 113, 26--43 (2017; Zbl 1355.65062) Full Text: DOI arXiv Link
Takane, Yoshio; Loisel, Sébastien On the PLS algorithm for multiple regression (PLS1). (English) Zbl 1366.62140 Abdi, Hervé (ed.) et al., The multiple facets of partial least squares methods. PLS, Paris, France, May 26–28, 2014. Cham: Springer (ISBN 978-3-319-40641-1/hbk; 978-3-319-40643-5/ebook). Springer Proceedings in Mathematics & Statistics 173, 17-28 (2016). MSC: 62J05 62C20 62H25 PDFBibTeX XMLCite \textit{Y. Takane} and \textit{S. Loisel}, Springer Proc. Math. Stat. 173, 17--28 (2016; Zbl 1366.62140) Full Text: DOI
Niu, Datian; Meng, Jiana Improving approximate singular triplets in Lanczos bidiagonalization method. (English) Zbl 1357.65045 Taiwanese J. Math. 20, No. 4, 943-956 (2016). MSC: 65F15 15A23 PDFBibTeX XMLCite \textit{D. Niu} and \textit{J. Meng}, Taiwanese J. Math. 20, No. 4, 943--956 (2016; Zbl 1357.65045) Full Text: DOI
Gazzola, Silvia; Novati, Paolo Inheritance of the discrete Picard condition in Krylov subspace methods. (English) Zbl 1353.65023 BIT 56, No. 3, 893-918 (2016). Reviewer: Constantin Popa (Constanţa) MSC: 65F10 65F22 PDFBibTeX XMLCite \textit{S. Gazzola} and \textit{P. Novati}, BIT 56, No. 3, 893--918 (2016; Zbl 1353.65023) Full Text: DOI
Greif, C.; Paige, C. C.; Titley-Peloquin, D.; Varah, J. M. Numerical equivalences among Krylov subspace algorithms for skew-symmetric matrices. (English) Zbl 1347.65062 SIAM J. Matrix Anal. Appl. 37, No. 3, 1071-1087 (2016). MSC: 65F10 65F50 PDFBibTeX XMLCite \textit{C. Greif} et al., SIAM J. Matrix Anal. Appl. 37, No. 3, 1071--1087 (2016; Zbl 1347.65062) Full Text: DOI
Gazzola, Silvia; Onunwor, Enyinda; Reichel, Lothar; Rodriguez, Giuseppe On the Lanczos and Golub-Kahan reduction methods applied to discrete ill-posed problems. (English) Zbl 1413.65120 Numer. Linear Algebra Appl. 23, No. 1, 187-204 (2016). MSC: 65F22 65F10 65F35 PDFBibTeX XMLCite \textit{S. Gazzola} et al., Numer. Linear Algebra Appl. 23, No. 1, 187--204 (2016; Zbl 1413.65120) Full Text: DOI
Wang, Xuansheng; Glineur, François; Lu, Linzhang; Van Dooren, Paul Extended Lanczos bidiagonalization algorithm for low rank approximation and its applications. (English) Zbl 1382.65107 J. Comput. Appl. Math. 301, 213-229 (2016). MSC: 65F15 PDFBibTeX XMLCite \textit{X. Wang} et al., J. Comput. Appl. Math. 301, 213--229 (2016; Zbl 1382.65107) Full Text: DOI
Bazán, Fermín S. V.; Kleefeld, Andreas; Leem, Koung Hee; Pelekanos, George Sampling method based projection approach for the reconstruction of 3D acoustically penetrable scatterers. (English) Zbl 1333.65124 Linear Algebra Appl. 495, 289-323 (2016). MSC: 65N21 35R30 35J05 65N38 65F22 PDFBibTeX XMLCite \textit{F. S. V. Bazán} et al., Linear Algebra Appl. 495, 289--323 (2016; Zbl 1333.65124) Full Text: DOI
Hochstenbach, Michiel E.; Reichel, Lothar; Yu, Xuebo A Golub-Kahan-type reduction method for matrix pairs. (English) Zbl 1329.65082 J. Sci. Comput. 65, No. 2, 767-789 (2015). MSC: 65F22 PDFBibTeX XMLCite \textit{M. E. Hochstenbach} et al., J. Sci. Comput. 65, No. 2, 767--789 (2015; Zbl 1329.65082) Full Text: DOI
Gaaf, Sarah W.; Hochstenbach, Michiel E. Probabilistic bounds for the matrix condition number with extended Lanczos bidiagonalization. (English) Zbl 1325.65051 SIAM J. Sci. Comput. 37, No. 5, S581-S601 (2015). MSC: 65F15 65F35 65F50 65F10 PDFBibTeX XMLCite \textit{S. W. Gaaf} and \textit{M. E. Hochstenbach}, SIAM J. Sci. Comput. 37, No. 5, S581--S601 (2015; Zbl 1325.65051) Full Text: DOI Link
Gazzola, Silvia; Novati, Paolo; Russo, Maria Rosaria On Krylov projection methods and Tikhonov regularization. (English) Zbl 1312.65065 ETNA, Electron. Trans. Numer. Anal. 44, 83-123 (2015). MSC: 65F22 65F10 PDFBibTeX XMLCite \textit{S. Gazzola} et al., ETNA, Electron. Trans. Numer. Anal. 44, 83--123 (2015; Zbl 1312.65065) Full Text: EMIS
Potts, Daniel; Tasche, Manfred Fast ESPRIT algorithms based on partial singular value decompositions. (English) Zbl 1302.65043 Appl. Numer. Math. 88, 31-45 (2015). MSC: 65D05 65F15 PDFBibTeX XMLCite \textit{D. Potts} and \textit{M. Tasche}, Appl. Numer. Math. 88, 31--45 (2015; Zbl 1302.65043) Full Text: DOI
Noschese, Silvia; Reichel, Lothar Inverse subspace problems with applications. (English) Zbl 1340.65069 Numer. Linear Algebra Appl. 21, No. 5, 589-603 (2014). Reviewer: Robert Plato (Siegen) MSC: 65F22 65F25 65F35 PDFBibTeX XMLCite \textit{S. Noschese} and \textit{L. Reichel}, Numer. Linear Algebra Appl. 21, No. 5, 589--603 (2014; Zbl 1340.65069) Full Text: DOI
Lu, Ling; Xu, Wei A fast rank-reduction algorithm based on block Hankel Hankel block matrix-vector multiplication with applications to seismic signal processing. (Chinese. English summary) Zbl 1313.65092 J. Tongji Univ., Nat. Sci. 42, No. 5, 807-815 (2014). MSC: 65F30 86A17 65F20 94A12 65T50 PDFBibTeX XMLCite \textit{L. Lu} and \textit{W. Xu}, J. Tongji Univ., Nat. Sci. 42, No. 5, 807--815 (2014; Zbl 1313.65092) Full Text: DOI
Niu, Datian; Yuan, Xuegang An implicitly restarted Lanczos bidiagonalization method with refined harmonic shifts for computing smallest singular triplets. (English) Zbl 1293.65057 J. Comput. Appl. Math. 260, 208-217 (2014). MSC: 65F15 PDFBibTeX XMLCite \textit{D. Niu} and \textit{X. Yuan}, J. Comput. Appl. Math. 260, 208--217 (2014; Zbl 1293.65057) Full Text: DOI
Erfani, Shervan; Tavakoli, Ali; Salkuyeh, Davod Khojasteh An efficient method to set up a Lanczos based preconditioner for discrete ill-posed problems. (English) Zbl 1426.65043 Appl. Math. Modelling 37, No. 20-21, 8742-8756 (2013). MSC: 65F08 65F22 65R20 PDFBibTeX XMLCite \textit{S. Erfani} et al., Appl. Math. Modelling 37, No. 20--21, 8742--8756 (2013; Zbl 1426.65043) Full Text: DOI
Hochstenbach, Michiel E. Probabilistic upper bounds for the matrix two-norm. (English) Zbl 1292.65037 J. Sci. Comput. 57, No. 3, 464-476 (2013). MSC: 65F15 15A42 65F35 65F50 PDFBibTeX XMLCite \textit{M. E. Hochstenbach}, J. Sci. Comput. 57, No. 3, 464--476 (2013; Zbl 1292.65037) Full Text: DOI Link
Baglama, James; Reichel, Lothar An implicitly restarted block Lanczos bidiagonalization method using Leja shifts. (English) Zbl 1269.65038 BIT 53, No. 2, 285-310 (2013). MSC: 65F20 PDFBibTeX XMLCite \textit{J. Baglama} and \textit{L. Reichel}, BIT 53, No. 2, 285--310 (2013; Zbl 1269.65038) Full Text: DOI
Barlow, Jesse L. Reorthogonalization for the Golub-Kahan-Lanczos bidiagonal reduction. (English) Zbl 1272.65034 Numer. Math. 124, No. 2, 237-278 (2013). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F25 65F15 15A18 65F20 PDFBibTeX XMLCite \textit{J. L. Barlow}, Numer. Math. 124, No. 2, 237--278 (2013; Zbl 1272.65034) Full Text: DOI
Zhang, Di; Huang, Ting-Zhu Generalized Tikhonov regularization method for large-scale linear inverse problems. (English) Zbl 1273.65066 J. Comput. Anal. Appl. 15, No. 7, 1317-1331 (2013). MSC: 65J10 65J20 65J22 PDFBibTeX XMLCite \textit{D. Zhang} and \textit{T.-Z. Huang}, J. Comput. Anal. Appl. 15, No. 7, 1317--1331 (2013; Zbl 1273.65066)
Martin, David R.; Reichel, Lothar Minimization of functionals on the solution of a large-scale discrete ill-posed problem. (English) Zbl 1262.65053 BIT 53, No. 1, 153-173 (2013). MSC: 65F22 65K05 90C05 90C06 PDFBibTeX XMLCite \textit{D. R. Martin} and \textit{L. Reichel}, BIT 53, No. 1, 153--173 (2013; Zbl 1262.65053) Full Text: DOI
Wang, Xuansheng; Chen, Zhen; Lu, Linzhang Lanczos bidiagonalization: a fast start for nonnegative matrix factorization. (Chinese. English summary) Zbl 1265.65045 J. Xiamen Univ., Nat. Sci. 51, No. 2, 149-152 (2012). MSC: 65F05 65F20 PDFBibTeX XMLCite \textit{X. Wang} et al., J. Xiamen Univ., Nat. Sci. 51, No. 2, 149--152 (2012; Zbl 1265.65045)
Wang, Xuansheng; Xie, Xiaoyao; Lu, Linzhang An effective initialization for orthogonal nonnegative matrix factorization. (English) Zbl 1265.15028 J. Comput. Math. 30, No. 1, 34-46 (2012). MSC: 15A23 65F25 15B48 PDFBibTeX XMLCite \textit{X. Wang} et al., J. Comput. Math. 30, No. 1, 34--46 (2012; Zbl 1265.15028) Full Text: DOI
Haber, Eldad; Magnant, Zhuojun; Lucero, Christian; Tenorio, Luis Numerical methods for \(A\)-optimal designs with a sparsity constraint for ill-posed inverse problems. (English) Zbl 1259.90135 Comput. Optim. Appl. 52, No. 1, 293-314 (2012). MSC: 90C30 PDFBibTeX XMLCite \textit{E. Haber} et al., Comput. Optim. Appl. 52, No. 1, 293--314 (2012; Zbl 1259.90135) Full Text: DOI
Niu, Datian; Yuan, Xuegang A harmonic Lanczos bidiagonalization method for computing interior singular triplets of large matrices. (English) Zbl 1246.65065 Appl. Math. Comput. 218, No. 14, 7459-7467 (2012). MSC: 65F20 PDFBibTeX XMLCite \textit{D. Niu} and \textit{X. Yuan}, Appl. Math. Comput. 218, No. 14, 7459--7467 (2012; Zbl 1246.65065) Full Text: DOI arXiv
Stoll, Martin A Krylov-Schur approach to the truncated SVD. (English) Zbl 1241.65040 Linear Algebra Appl. 436, No. 8, 2795-2806 (2012). MSC: 65F20 PDFBibTeX XMLCite \textit{M. Stoll}, Linear Algebra Appl. 436, No. 8, 2795--2806 (2012; Zbl 1241.65040) Full Text: DOI
Niu, Datian Properties and application of harmonic Ritz pairs in a special kind of subspaces. (Chinese. English summary) Zbl 1225.15012 J. Dalian Nationalities Univ. 12, No. 5, 443-445 (2010). MSC: 15A18 65F20 PDFBibTeX XMLCite \textit{D. Niu}, J. Dalian Nationalities Univ. 12, No. 5, 443--445 (2010; Zbl 1225.15012)
Jia, Zhongxiao; Niu, Datian A refined harmonic Lanczos bidiagonalization method and an implicitly restarted algorithm for computing the smallest singular triplets of large matrices. (English) Zbl 1215.65072 SIAM J. Sci. Comput. 32, No. 2, 714-744 (2010). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F20 65F15 PDFBibTeX XMLCite \textit{Z. Jia} and \textit{D. Niu}, SIAM J. Sci. Comput. 32, No. 2, 714--744 (2010; Zbl 1215.65072) Full Text: DOI arXiv
Rezghi, Mansoor; Hosseini, S. M. Lanczos based preconditioner for discrete ill-posed problems. (English) Zbl 1190.65049 Computing 88, No. 1-2, 79-96 (2010). MSC: 65F08 65F22 PDFBibTeX XMLCite \textit{M. Rezghi} and \textit{S. M. Hosseini}, Computing 88, No. 1--2, 79--96 (2010; Zbl 1190.65049) Full Text: DOI
Lai, Jiangzhou; Lu, Linzhang An implicitly restarted Lanczos bidiagonalization method with refined vector. (Chinese. English summary) Zbl 1224.65107 J. Xiamen Univ., Nat. Sci. 48, No. 2, 153-159 (2009). MSC: 65F20 65F25 PDFBibTeX XMLCite \textit{J. Lai} and \textit{L. Lu}, J. Xiamen Univ., Nat. Sci. 48, No. 2, 153--159 (2009; Zbl 1224.65107)
Reichel, Lothar; Ye, Qiang Simple square smoothing regularization operators. (English) Zbl 1171.65033 ETNA, Electron. Trans. Numer. Anal. 33(2008-2009), 63-83 (2009). MSC: 65F22 65F10 65R32 PDFBibTeX XMLCite \textit{L. Reichel} and \textit{Q. Ye}, ETNA, Electron. Trans. Numer. Anal. 33, 63--83 (2009; Zbl 1171.65033) Full Text: EuDML EMIS
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
Browne, Kevin; Qiao, Sanzheng; Wei, Yimin A Lanczos bidiagonalization algorithm for Hankel matrices. (English) Zbl 1158.65027 Linear Algebra Appl. 430, No. 5-6, 1531-1543 (2009). MSC: 65F20 65F25 PDFBibTeX XMLCite \textit{K. Browne} et al., Linear Algebra Appl. 430, No. 5--6, 1531--1543 (2009; Zbl 1158.65027) Full Text: DOI
Hernández, Vicente; Román, José E.; Tomás, Andrés A robust and efficient parallel SVD solver based on restarted Lanczos bidiagonalization. (English) Zbl 1171.65382 ETNA, Electron. Trans. Numer. Anal. 31, 68-85 (2008). MSC: 65F20 65F50 65F15 65F25 PDFBibTeX XMLCite \textit{V. Hernández} et al., ETNA, Electron. Trans. Numer. Anal. 31, 68--85 (2008; Zbl 1171.65382) Full Text: EuDML EMIS
Chung, Julianne; Nagy, James G.; O’Leary, Dianne P. A weighted-GCV method for Lanczos-hybrid regularization. (English) Zbl 1171.65029 ETNA, Electron. Trans. Numer. Anal. 28(2007-2008), 149-167 (2008). MSC: 65F20 65F30 PDFBibTeX XMLCite \textit{J. Chung} et al., ETNA, Electron. Trans. Numer. Anal. 28, 149--167 (2008; Zbl 1171.65029) Full Text: EuDML EMIS
Niu, Datian; Jia, Zhongxiao; Wang, Kanmin A refined harmonic Lanczos bidiagonalization for computing smallest singular triplets. (Chinese. English summary) Zbl 1174.65377 Math. Numer. Sin. 30, No. 3, 311-326 (2008). MSC: 65F20 15A18 PDFBibTeX XMLCite \textit{D. Niu} et al., Math. Numer. Sin. 30, No. 3, 311--326 (2008; Zbl 1174.65377)
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
Hnětynková, Iveta; Strakoš, Zdeněk Lanczos tridiagonalization and core problems. (English) Zbl 1111.65041 Linear Algebra Appl. 421, No. 2-3, 243-251 (2007). MSC: 65F30 65F10 65F25 PDFBibTeX XMLCite \textit{I. Hnětynková} and \textit{Z. Strakoš}, Linear Algebra Appl. 421, No. 2--3, 243--251 (2007; Zbl 1111.65041) Full Text: DOI
Baglama, James; Reichel, Lothar Augmented implicitly restarted Lanczos bidiagonalization methods. (English) Zbl 1087.65039 SIAM J. Sci. Comput. 27, No. 1, 19-42 (2005). MSC: 65F20 65F10 65F50 PDFBibTeX XMLCite \textit{J. Baglama} and \textit{L. Reichel}, SIAM J. Sci. Comput. 27, No. 1, 19--42 (2005; Zbl 1087.65039) Full Text: DOI
Eldén, Lars Partial least-squares vs. Lanczos bidiagonalization. I: Analysis of a projection method for multiple regression. (English) Zbl 1429.62288 Comput. Stat. Data Anal. 46, No. 1, 11-31 (2004). MSC: 62J05 62J07 62H25 PDFBibTeX XMLCite \textit{L. Eldén}, Comput. Stat. Data Anal. 46, No. 1, 11--31 (2004; Zbl 1429.62288) Full Text: DOI
Pourquier, Olivier; Sadkane, Miloud On the normwise backward error of large underdeterminded least squares problems. (English) Zbl 1056.65033 Int. J. Pure Appl. Math. 14, No. 3, 365-376 (2004). Reviewer: Prem Narain (Faridabad) MSC: 65F20 65F30 65F50 PDFBibTeX XMLCite \textit{O. Pourquier} and \textit{M. Sadkane}, Int. J. Pure Appl. Math. 14, No. 3, 365--376 (2004; Zbl 1056.65033)
Jia, Zhongxiao; Niu, Datian An implicitly restarted refined bidiagonalization Lanczos method for computing a partial singular value decomposition. (English) Zbl 1063.65030 SIAM J. Matrix Anal. Appl. 25, No. 1, 246-265 (2003). MSC: 65F20 PDFBibTeX XMLCite \textit{Z. Jia} and \textit{D. Niu}, SIAM J. Matrix Anal. Appl. 25, No. 1, 246--265 (2003; Zbl 1063.65030) Full Text: DOI
Calvetti, Daniela; Reichel, Lothar Tikhonov regularization of large linear problems. (English) Zbl 1038.65048 BIT 43, No. 2, 263-283 (2003). Reviewer: Bernd Hofmann (Chemnitz) MSC: 65J10 65R20 65R30 45B05 65J20 47A52 PDFBibTeX XMLCite \textit{D. Calvetti} and \textit{L. Reichel}, BIT 43, No. 2, 263--283 (2003; Zbl 1038.65048) Full Text: DOI
Malyshev, A.; Sadkane, M. Condition numbers for Lanczos bidiagonalization with complete reorthogonalization. (English) Zbl 1027.65051 Linear Algebra Appl. 371, 315-331 (2003). MSC: 65F25 65F35 PDFBibTeX XMLCite \textit{A. Malyshev} and \textit{M. Sadkane}, Linear Algebra Appl. 371, 315--331 (2003; Zbl 1027.65051) Full Text: DOI
Calvetti, D.; Hansen, P. C.; Reichel, L. \(L\)-curve curvature bounds via Lanczos bidiagonalization. (English) Zbl 1029.65041 ETNA, Electron. Trans. Numer. Anal. 14, 20-35 (2002). Reviewer: S.Zlobec (Montreal) MSC: 65F22 PDFBibTeX XMLCite \textit{D. Calvetti} et al., ETNA, Electron. Trans. Numer. Anal. 14, 20--35 (2002; Zbl 1029.65041) Full Text: EuDML EMIS
Malyshev, A.; Sadkane, M. Computation of optimal backward perturbation bounds for large sparse linear least squares problems. (English) Zbl 0994.65041 BIT 41, No. 4, 739-747 (2001). Reviewer: F.Szidarovszky (Tucson) MSC: 65F20 65F50 PDFBibTeX XMLCite \textit{A. Malyshev} and \textit{M. Sadkane}, BIT 41, No. 4, 739--747 (2001; Zbl 0994.65041) Full Text: DOI
Simon, Horst D.; Zha, Hongyuan Low-rank matrix approximation using the Lanczos bidiagonalization process with applications. (English) Zbl 0962.65038 SIAM J. Sci. Comput. 21, No. 6, 2257-2274 (2000). Reviewer: Miloslav Znojil (Řež) MSC: 65F20 65F50 PDFBibTeX XMLCite \textit{H. D. Simon} and \textit{H. Zha}, SIAM J. Sci. Comput. 21, No. 6, 2257--2274 (2000; Zbl 0962.65038) Full Text: DOI
Calvetti, D.; Golub, G. H.; Reichel, L. Estimation of the \(L\)-curve via Lanczos bidiagonalization. (English) Zbl 0945.65044 BIT 39, No. 4, 603-619 (1999). Reviewer: Petko Hr.Petkov (Sofia) MSC: 65F22 PDFBibTeX XMLCite \textit{D. Calvetti} et al., BIT 39, No. 4, 603--619 (1999; Zbl 0945.65044) Full Text: DOI
Björck, Åke; Elfving, Tommy; Strakous, Zdenuek Stability of conjugate gradient and Lanczos methods for linear least squares problems. (English) Zbl 0924.65035 SIAM J. Matrix Anal. Appl. 19, No. 3, 720-736 (1998). Reviewer: Juan Pedro Milaszewicz (Ioannina) MSC: 65F20 65F10 PDFBibTeX XMLCite \textit{Å. Björck} et al., SIAM J. Matrix Anal. Appl. 19, No. 3, 720--736 (1998; Zbl 0924.65035) Full Text: DOI
Zha, Hongyuan Computing the generalized singular values/vectors of large sparse or structured matrix pairs. (English) Zbl 0856.65041 Numer. Math. 72, No. 3, 391-417 (1996). Reviewer: P.Narain (Bombay) MSC: 65F20 65F15 65F50 PDFBibTeX XMLCite \textit{H. Zha}, Numer. Math. 72, No. 3, 391--417 (1996; Zbl 0856.65041) Full Text: DOI
Saunders, Michael A. Solution of sparse rectangular systems using LSQR and Craig. (English) Zbl 0844.65029 BIT 35, No. 4, 588-604 (1995). Reviewer: N.Köckler (Paderborn) MSC: 65F20 65F50 PDFBibTeX XMLCite \textit{M. A. Saunders}, BIT 35, No. 4, 588--604 (1995; Zbl 0844.65029) Full Text: DOI
Hansen, P. C.; Hanke, M. A Lanczos algorithm for computing the largest quotient singular values in regularization problems. (English) Zbl 0826.65037 Moonen, Marc (ed.) et al., SVD and signal processing III: algorithms, architectures and applications. Based on contributions presented at the 3rd international workshop on SVD and signal processing, Leuven (Belgium), 22-25 August 1994. Amsterdam: Elsevier. 131-138 (1995). MSC: 65F20 65F15 PDFBibTeX XMLCite \textit{P. C. Hansen} and \textit{M. Hanke}, in: SVD and signal processing III: algorithms, architectures and applications. Based on contributions presented at the 3rd international workshop on SVD and signal processing, Leuven (Belgium), 22-25 August 1994. Amsterdam: Elsevier. 131--138 (1995; Zbl 0826.65037)
Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O’Leary, D. P. Regularization by truncated total least squares. (English) Zbl 0819.65066 Lewis, John G. (ed.), Applied linear algebra. Proceedings of the 5th SIAM conference, held in Snowbird, UT, USA, June 15-18, 1994. Philadelphia, PA: SIAM. 250-254 (1994). MSC: 65F20 65F10 PDFBibTeX XMLCite \textit{R. D. Fierro} et al., in: Applied linear algebra. Proceedings of the 5th SIAM conference, held in Snowbird, UT, USA, June 15-18, 1994. Philadelphia, PA: SIAM. 250--254 (1994; Zbl 0819.65066)
Björck, Åke; Grimme, Eric; van Dooren, Paul An implicit shift bidiagonalization algorithm for ill-posed systems. (English) Zbl 0821.65023 BIT 34, No. 4, 510-534 (1994). Reviewer: Xie Shenquan (Xiangtan) MSC: 65F20 65F10 PDFBibTeX XMLCite \textit{Å. Björck} et al., BIT 34, No. 4, 510--534 (1994; Zbl 0821.65023) Full Text: DOI
Björck, Åke A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations. (English) Zbl 0658.65041 BIT 28, No. 3, 659-670 (1988). Reviewer: G.Maeß MSC: 65F20 65N22 PDFBibTeX XMLCite \textit{Å. Björck}, BIT 28, No. 3, 659--670 (1988; Zbl 0658.65041) Full Text: DOI
Eldén, Lars An efficient algorithm for the regularization of ill-conditioned least squares problems with triangular Toeplitz matrix. (English) Zbl 0546.65013 SIAM J. Sci. Stat. Comput. 5, 229-236 (1984). Reviewer: N.Köckler MSC: 65F20 65R20 45D05 62M10 PDFBibTeX XMLCite \textit{L. Eldén}, SIAM J. Sci. Stat. Comput. 5, 229--236 (1984; Zbl 0546.65013) Full Text: DOI
Cullum, Jane; Willoughby, Ralph A.; Lake, Mark A Lanczos algorithm for computing singular values and vectors of large matrices. (English) Zbl 0518.65020 SIAM J. Sci. Stat. Comput. 4, 197-215 (1983). MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{J. Cullum} et al., SIAM J. Sci. Stat. Comput. 4, 197--215 (1983; Zbl 0518.65020) Full Text: DOI
O’Leary, Dianne P.; Simmons, John A. A bidiagonalization-regularization procedure for large scale discretizations of ill-posed problems. (English) Zbl 0469.65089 SIAM J. Sci. Stat. Comput. 2, 474-489 (1981). MSC: 65R20 65F20 45B05 PDFBibTeX XMLCite \textit{D. P. O'Leary} and \textit{J. A. Simmons}, SIAM J. Sci. Stat. Comput. 2, 474--489 (1981; Zbl 0469.65089) Full Text: DOI