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
Chung, Matthias; Renaut, Rosemary A. A variable projection method for large-scale inverse problems with \(\ell^1\) regularization. (English) Zbl 1528.65031 Appl. Numer. Math. 192, 297-318 (2023). MSC: 65K05 90C25 65F22 94A08 PDFBibTeX XMLCite \textit{M. Chung} and \textit{R. A. Renaut}, Appl. Numer. Math. 192, 297--318 (2023; Zbl 1528.65031) Full Text: DOI
Español, Malena I.; Pasha, Mirjeta Variable projection methods for separable nonlinear inverse problems with general-form Tikhonov regularization. (English) Zbl 07707676 Inverse Probl. 39, No. 8, Article ID 084002, 25 p. (2023). MSC: 65Fxx 90Cxx 65Kxx PDFBibTeX XMLCite \textit{M. I. Español} and \textit{M. Pasha}, Inverse Probl. 39, No. 8, Article ID 084002, 25 p. (2023; Zbl 07707676) Full Text: DOI
Tian, Lin Parameter choice strategies for error expressions and the numerical stability of Tikhonov-regularized approximation formulae. (English) Zbl 1524.65180 Comput. Appl. Math. 42, No. 4, Paper No. 202, 22 p. (2023). MSC: 65F22 65D05 65G50 PDFBibTeX XMLCite \textit{L. Tian}, Comput. Appl. Math. 42, No. 4, Paper No. 202, 22 p. (2023; Zbl 1524.65180) Full Text: DOI
Alavi, Javad; Aminikhah, Hossein Some properties of orthogonal linear splines and their applications to inverse problems. (English) Zbl 1509.65008 Appl. Anal. 102, No. 3, 739-769 (2023). MSC: 65D07 65N21 65F22 47A52 47J06 PDFBibTeX XMLCite \textit{J. Alavi} and \textit{H. Aminikhah}, Appl. Anal. 102, No. 3, 739--769 (2023; Zbl 1509.65008) Full Text: DOI
Buccini, Alessandro; Reichel, Lothar Limited memory restarted \(\ell^p\)-\(\ell^q\) minimization methods using generalized Krylov subspaces. (English) Zbl 1518.65030 Adv. Comput. Math. 49, No. 2, Paper No. 26, 26 p. (2023). MSC: 65F10 65F25 65R32 90C26 PDFBibTeX XMLCite \textit{A. Buccini} and \textit{L. Reichel}, Adv. Comput. Math. 49, No. 2, Paper No. 26, 26 p. (2023; Zbl 1518.65030) 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
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
Havelková, Eva; Hnětynková, Iveta Iterative hybrid regularization for extremely noisy full models in single particle analysis. (English) Zbl 1505.65174 Linear Algebra Appl. 656, 131-157 (2023). MSC: 65F22 65F50 PDFBibTeX XMLCite \textit{E. Havelková} and \textit{I. Hnětynková}, Linear Algebra Appl. 656, 131--157 (2023; Zbl 1505.65174) Full Text: DOI
Buccini, Alessandro; Pragliola, Monica; Reichel, Lothar; Sgallari, Fiorella A comparison of parameter choice rules for \(\ell^p\)-\(\ell^q\) minimization. (English) Zbl 1500.65027 Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 68, No. 2, 441-463 (2022). MSC: 65K05 65F22 94A08 PDFBibTeX XMLCite \textit{A. Buccini} et al., Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 68, No. 2, 441--463 (2022; Zbl 1500.65027) Full Text: DOI
Jian, Yuan Subspaces analysis for random projection UTV framework. (English) Zbl 1508.65035 SIAM J. Matrix Anal. Appl. 43, No. 3, 1291-1307 (2022). MSC: 65F20 15A18 65F25 PDFBibTeX XMLCite \textit{Y. Jian}, SIAM J. Matrix Anal. Appl. 43, No. 3, 1291--1307 (2022; Zbl 1508.65035) Full Text: DOI
Che, Maolin; Wei, Yimin An efficient algorithm for computing the approximate t-URV and its applications. (English) Zbl 1498.65062 J. Sci. Comput. 92, No. 3, Paper No. 93, 27 p. (2022). MSC: 65F99 15A69 PDFBibTeX XMLCite \textit{M. Che} and \textit{Y. Wei}, J. Sci. Comput. 92, No. 3, Paper No. 93, 27 p. (2022; Zbl 1498.65062) Full Text: DOI
Hansen, Per Christian; Hayami, Ken; Morikuni, Keiichi GMRES methods for tomographic reconstruction with an unmatched back projector. (English) Zbl 1489.65060 J. Comput. Appl. Math. 413, Article ID 114352, 20 p. (2022). MSC: 65F22 65F10 94A08 PDFBibTeX XMLCite \textit{P. C. Hansen} et al., J. Comput. Appl. Math. 413, Article ID 114352, 20 p. (2022; Zbl 1489.65060) Full Text: DOI arXiv
Bianchi, Davide; Buccini, Alessandro; Donatelli, Marco; Randazzo, Emma Graph Laplacian for image deblurring. (English) Zbl 1487.65203 ETNA, Electron. Trans. Numer. Anal. 55, 169-186 (2022). MSC: 65R32 65F22 94A08 PDFBibTeX XMLCite \textit{D. Bianchi} et al., ETNA, Electron. Trans. Numer. Anal. 55, 169--186 (2022; Zbl 1487.65203) Full Text: DOI arXiv
Ben Belgacem, Faker; Girault, Vivette; Jelassi, Faten Full discretization of Cauchy’s problem by Lavrentiev-finite element method. (English) Zbl 07498293 SIAM J. Numer. Anal. 60, No. 2, 558-584 (2022). MSC: 65-XX 35R25 65F22 65N30 PDFBibTeX XMLCite \textit{F. Ben Belgacem} et al., SIAM J. Numer. Anal. 60, No. 2, 558--584 (2022; Zbl 07498293) Full Text: DOI
Zare, Hossein; Hajarian, Masoud An efficient Gauss-Newton algorithm for solving regularized total least squares problems. (English) Zbl 1490.65073 Numer. Algorithms 89, No. 3, 1049-1073 (2022). MSC: 65F22 65F20 PDFBibTeX XMLCite \textit{H. Zare} and \textit{M. Hajarian}, Numer. Algorithms 89, No. 3, 1049--1073 (2022; Zbl 1490.65073) Full Text: DOI
Petkov, Petko H.; Konstantinov, Mihail M. The numerical Jordan form. (English) Zbl 1482.65059 Linear Algebra Appl. 638, 1-45 (2022). MSC: 65F15 65F22 15A20 15A21 47A55 PDFBibTeX XMLCite \textit{P. H. Petkov} and \textit{M. M. Konstantinov}, Linear Algebra Appl. 638, 1--45 (2022; Zbl 1482.65059) Full Text: DOI
Luiken, Nick; van Leeuwen, Tristan Relaxed regularization for linear inverse problems. (English) Zbl 1490.65071 SIAM J. Sci. Comput. 43, No. 5, S269-S292 (2021). MSC: 65F22 65F10 15A18 15A29 PDFBibTeX XMLCite \textit{N. Luiken} and \textit{T. van Leeuwen}, SIAM J. Sci. Comput. 43, No. 5, S269--S292 (2021; Zbl 1490.65071) Full Text: DOI
van Lith, Bart S.; Hansen, Per Christian; Hochstenbach, Michiel E. A twin error gauge for Kaczmarz’s iterations. (English) Zbl 1490.65072 SIAM J. Sci. Comput. 43, No. 5, S173-S199 (2021). MSC: 65F22 65F10 65R32 65F15 PDFBibTeX XMLCite \textit{B. S. van Lith} et al., SIAM J. Sci. Comput. 43, No. 5, S173--S199 (2021; Zbl 1490.65072) 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
Duan, Shuyong; Yang, Botao; Wang, Fang; Liu, Guirong Determination of singular value truncation threshold for regularization in ill-posed problems. (English) Zbl 1469.65080 Inverse Probl. Sci. Eng. 29, No. 8, 1127-1157 (2021). MSC: 65F22 65F15 44A12 PDFBibTeX XMLCite \textit{S. Duan} et al., Inverse Probl. Sci. Eng. 29, No. 8, 1127--1157 (2021; Zbl 1469.65080) Full Text: DOI
Luiken, Nick; van Leeuwen, Tristan Relaxed regularization for linear inverse problems. (English) Zbl 1512.65071 SIAM J. Sci. Comput. 43, No. 3, S269-S292 (2021). MSC: 65F22 65F10 15A18 15A29 PDFBibTeX XMLCite \textit{N. Luiken} and \textit{T. van Leeuwen}, SIAM J. Sci. Comput. 43, No. 3, S269--S292 (2021; Zbl 1512.65071) Full Text: DOI arXiv
van Lith, Bart S.; Hansen, Per Christian; Hochstenbach, Michiel E. A twin error gauge for Kaczmarz’s iterations. (English) Zbl 1512.65072 SIAM J. Sci. Comput. 43, No. 3, S173-S199 (2021). MSC: 65F22 65F10 65R32 65F15 PDFBibTeX XMLCite \textit{B. S. van Lith} et al., SIAM J. Sci. Comput. 43, No. 3, S173--S199 (2021; Zbl 1512.65072) Full Text: DOI arXiv
Zhang, Jianjun; Nagy, James G. An effective alternating direction method of multipliers for color image restoration. (English) Zbl 1471.65016 Appl. Numer. Math. 164, 43-56 (2021). MSC: 65D18 65F22 65K10 94A08 PDFBibTeX XMLCite \textit{J. Zhang} and \textit{J. G. Nagy}, Appl. Numer. Math. 164, 43--56 (2021; Zbl 1471.65016) Full Text: DOI
Cui, Jingjing; Peng, Guohua; Lu, Quan; Huang, Zhengge Modified special HSS method for discrete ill-posed problems and image restoration. (English) Zbl 1480.65092 Int. J. Comput. Math. 97, No. 4, 739-758 (2020). MSC: 65F22 65F10 65D18 94A08 PDFBibTeX XMLCite \textit{J. Cui} et al., Int. J. Comput. Math. 97, No. 4, 739--758 (2020; Zbl 1480.65092) Full Text: DOI
Brown, Richard D.; Bardsley, Johnathan M.; Cui, Tiangang Semivariogram methods for modeling Whittle-Matérn priors in Bayesian inverse problems. (English) Zbl 1475.62120 Inverse Probl. 36, No. 5, Article ID 055006, 27 p. (2020). MSC: 62F15 62H35 60H15 65F22 PDFBibTeX XMLCite \textit{R. D. Brown} et al., Inverse Probl. 36, No. 5, Article ID 055006, 27 p. (2020; Zbl 1475.62120) Full Text: DOI arXiv
Jia, Zhongxiao The low rank approximations and Ritz values in LSQR for linear discrete ill-posed problem. (English) Zbl 07371359 Inverse Probl. 36, No. 4, Article ID 045013, 31 p. (2020). MSC: 65Fxx 65Jxx 65Rxx 65-XX 35Rxx PDFBibTeX XMLCite \textit{Z. Jia}, Inverse Probl. 36, No. 4, Article ID 045013, 31 p. (2020; Zbl 07371359) Full Text: DOI arXiv
Jia, Zhongxiao Regularization properties of Krylov iterative solvers CGME and LSMR for linear discrete ill-posed problems with an application to truncated randomized SVDs. (English) Zbl 1455.65062 Numer. Algorithms 85, No. 4, 1281-1310 (2020). MSC: 65F22 65F10 65F15 65F55 15A18 PDFBibTeX XMLCite \textit{Z. Jia}, Numer. Algorithms 85, No. 4, 1281--1310 (2020; Zbl 1455.65062) Full Text: DOI arXiv
Jia, Zhongxiao Regularization properties of LSQR for linear discrete ill-posed problems in the multiple singular value case and best, near best and general low rank approximations. (English) Zbl 1452.65075 Inverse Probl. 36, No. 8, Article ID 085009, 38 p. (2020). MSC: 65F22 65F15 PDFBibTeX XMLCite \textit{Z. Jia}, Inverse Probl. 36, No. 8, Article ID 085009, 38 p. (2020; Zbl 1452.65075) Full Text: DOI arXiv
Buccini, A.; Pasha, M.; Reichel, L. Modulus-based iterative methods for constrained \(\ell_p\)-\(\ell_q\) minimization. (English) Zbl 1451.65072 Inverse Probl. 36, No. 8, Article ID 084001, 26 p. (2020). MSC: 65K05 65F22 90C25 PDFBibTeX XMLCite \textit{A. Buccini} et al., Inverse Probl. 36, No. 8, Article ID 084001, 26 p. (2020; Zbl 1451.65072) Full Text: DOI
Jia, Zhongxiao; Yang, Yanfei A joint bidiagonalization based iterative algorithm for large scale general-form Tikhonov regularization. (English) Zbl 1452.65076 Appl. Numer. Math. 157, 159-177 (2020). MSC: 65F22 65F15 15A18 PDFBibTeX XMLCite \textit{Z. Jia} and \textit{Y. Yang}, Appl. Numer. Math. 157, 159--177 (2020; Zbl 1452.65076) Full Text: DOI arXiv
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
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
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
Mesgarani, Hamid; Azari, Yaqub Numerical investigation of Fredholm integral equation of the first kind with noisy data. (English) Zbl 1452.65409 Math. Sci., Springer 13, No. 3, 267-278 (2019). MSC: 65R20 65F22 65N20 65N21 PDFBibTeX XMLCite \textit{H. Mesgarani} and \textit{Y. Azari}, Math. Sci., Springer 13, No. 3, 267--278 (2019; Zbl 1452.65409) 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
Martinsson, P. G.; Quintana-Ortí, G.; Heavner, N. randUTV: a blocked randomized algorithm for computing a rank-revealing UTV factorization. (English) Zbl 1471.65031 ACM Trans. Math. Softw. 45, No. 1, Article No. 4, 26 p. (2019). MSC: 65F99 68W20 PDFBibTeX XMLCite \textit{P. G. Martinsson} et al., ACM Trans. Math. Softw. 45, No. 1, Article No. 4, 26 p. (2019; Zbl 1471.65031) Full Text: DOI arXiv
Zeng, Zhonggang On the sensitivity of singular and ill-conditioned linear systems. (English) Zbl 1420.65055 SIAM J. Matrix Anal. Appl. 40, No. 3, 918-942 (2019). MSC: 65F22 65F35 15A12 15A06 PDFBibTeX XMLCite \textit{Z. Zeng}, SIAM J. Matrix Anal. Appl. 40, No. 3, 918--942 (2019; Zbl 1420.65055) Full Text: DOI arXiv
Zhang, Xiongjun; Ng, Michael K. A fast algorithm for solving linear inverse problems with uniform noise removal. (English) Zbl 1416.65108 J. Sci. Comput. 79, No. 2, 1214-1240 (2019). MSC: 65F22 94A08 94A12 90C25 PDFBibTeX XMLCite \textit{X. Zhang} and \textit{M. K. Ng}, J. Sci. Comput. 79, No. 2, 1214--1240 (2019; Zbl 1416.65108) Full Text: DOI
Kabashima, Kenta; Wu, Tianxiong; Nara, Takaaki Reconstruction of current dipoles based on tensor decomposition of multipole coefficients. (English) Zbl 1448.65207 JSIAM Lett. 11, 29-32 (2019). MSC: 65N21 65F99 15A23 PDFBibTeX XMLCite \textit{K. Kabashima} et al., JSIAM Lett. 11, 29--32 (2019; Zbl 1448.65207) Full Text: DOI
Bubba, Tatiana A.; Porta, Federica; Zanghirati, Gaetano; Bonettini, Silvia A nonsmooth regularization approach based on shearlets for Poisson noise removal in ROI tomography. (English) Zbl 1426.92036 Appl. Math. Comput. 318, 131-152 (2018). MSC: 92C55 42C40 44A12 65F22 65K10 PDFBibTeX XMLCite \textit{T. A. Bubba} et al., Appl. Math. Comput. 318, 131--152 (2018; Zbl 1426.92036) Full Text: DOI
Erbay, Hasan; Varçin, Fatih; Horasan, Fahrettin; Biçer, Cenker Block classical Gram-Schmidt-based block updating in low-rank matrix approximation. (English) Zbl 1424.65049 Turk. J. Math. 42, No. 4, 1779-1794 (2018). MSC: 65F30 65F25 PDFBibTeX XMLCite \textit{H. Erbay} et al., Turk. J. Math. 42, No. 4, 1779--1794 (2018; Zbl 1424.65049) Full Text: DOI
Zhdanov, Aleksandr Ivanovich Implicit iterative schemes based on singular decomposition and regularizing algorithms. (English) Zbl 1424.65037 Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki 22, No. 3, 549-556 (2018). MSC: 65F10 65F22 PDFBibTeX XMLCite \textit{A. I. Zhdanov}, Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki 22, No. 3, 549--556 (2018; Zbl 1424.65037) Full Text: DOI MNR
Aminikhah, Hossein; Yousefi, Mahsa A special generalized HSS method for discrete ill-posed problems. (English) Zbl 1405.65041 Comput. Appl. Math. 37, No. 2, 1507-1523 (2018). Reviewer: Constantin Popa (Constanţa) MSC: 65F10 94A08 65F22 15B57 PDFBibTeX XMLCite \textit{H. Aminikhah} and \textit{M. Yousefi}, Comput. Appl. Math. 37, No. 2, 1507--1523 (2018; Zbl 1405.65041) Full Text: DOI
Jia, Zhongxiao; Yang, Yanfei Modified truncated randomized singular value decomposition (MTRSVD) algorithms for large scale discrete ill-posed problems with general-form regularization. (English) Zbl 1518.65037 Inverse Probl. 34, No. 5, Article ID 055013, 28 p. (2018). MSC: 65F22 65F15 PDFBibTeX XMLCite \textit{Z. Jia} and \textit{Y. Yang}, Inverse Probl. 34, No. 5, Article ID 055013, 28 p. (2018; Zbl 1518.65037) Full Text: DOI arXiv
Aminikhah, H.; Yousefi, M. Preconditioned RRGMRES for discrete ill-posed problems. (English) Zbl 1404.65028 Int. J. Comput. Methods 15, No. 4, Article ID 1850023, 13 p. (2018). MSC: 65F22 65F08 65F10 PDFBibTeX XMLCite \textit{H. Aminikhah} and \textit{M. Yousefi}, Int. J. Comput. Methods 15, No. 4, Article ID 1850023, 13 p. (2018; Zbl 1404.65028) Full Text: DOI
Calvetti, D.; Pitolli, F.; Somersalo, E.; Vantaggi, B. Bayes meets Krylov: statistically inspired preconditioners for CGLS. (English) Zbl 1392.65047 SIAM Rev. 60, No. 2, 429-461 (2018). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F10 65F08 65N22 65F22 PDFBibTeX XMLCite \textit{D. Calvetti} et al., SIAM Rev. 60, No. 2, 429--461 (2018; Zbl 1392.65047) 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
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
Huang, Yi; Jia, Zhongxiao On regularizing effects of MINRES and MR-II for large scale symmetric discrete ill-posed problems. (English) Zbl 1372.65119 J. Comput. Appl. Math. 320, 145-163 (2017). MSC: 65F22 65F10 PDFBibTeX XMLCite \textit{Y. Huang} and \textit{Z. Jia}, J. Comput. Appl. Math. 320, 145--163 (2017; Zbl 1372.65119) Full Text: DOI arXiv
Renaut, Rosemary A.; Horst, Michael; Wang, Yang; Cochran, Douglas; Hansen, Jakob Efficient estimation of regularization parameters via downsampling and the singular value expansion, downsampling regularization parameter estimation. (English) Zbl 1367.65061 BIT 57, No. 2, 499-529 (2017). MSC: 65F22 65R20 45B05 65F20 65R30 65R32 PDFBibTeX XMLCite \textit{R. A. Renaut} et al., BIT 57, No. 2, 499--529 (2017; Zbl 1367.65061) Full Text: DOI arXiv
Zwaan, Ian N.; Hochstenbach, Michiel E. Multidirectional subspace expansion for one-parameter and multiparameter Tikhonov regularization. (English) Zbl 1370.65021 J. Sci. Comput. 70, No. 3, 990-1009 (2017). Reviewer: Murli Gupta (Washington, D. C.) MSC: 65F22 65F08 PDFBibTeX XMLCite \textit{I. N. Zwaan} and \textit{M. E. Hochstenbach}, J. Sci. Comput. 70, No. 3, 990--1009 (2017; Zbl 1370.65021) Full Text: DOI
Pisarenco, Maxim; Setija, Irwan D. Compact discrepancy and chi-squared principles for over-determined inverse problems. (English) Zbl 1368.65064 J. Inverse Ill-Posed Probl. 25, No. 3, 357-372 (2017). MSC: 65F20 65F22 PDFBibTeX XMLCite \textit{M. Pisarenco} and \textit{I. D. Setija}, J. Inverse Ill-Posed Probl. 25, No. 3, 357--372 (2017; Zbl 1368.65064) Full Text: DOI
Bai, Zhong-Zhi; Buccini, Alessandro; Hayami, Ken; Reichel, Lothar; Yin, Jun-Feng; Zheng, Ning Modulus-based iterative methods for constrained Tikhonov regularization. (English) Zbl 1360.65112 J. Comput. Appl. Math. 319, 1-13 (2017). MSC: 65F22 65F10 65D18 65K10 90C20 PDFBibTeX XMLCite \textit{Z.-Z. Bai} et al., J. Comput. Appl. Math. 319, 1--13 (2017; Zbl 1360.65112) Full Text: DOI Link
Wei, Yimin; Xie, Pengpeng; Zhang, Liping Tikhonov regularization and randomized GSVD. (English) Zbl 1339.65057 SIAM J. Matrix Anal. Appl. 37, No. 2, 649-675 (2016). MSC: 65F22 PDFBibTeX XMLCite \textit{Y. Wei} et al., SIAM J. Matrix Anal. Appl. 37, No. 2, 649--675 (2016; Zbl 1339.65057) Full Text: DOI
Revunova, E. G. Analytical study of error components for solving discrete ill-posed problems using random projections. (English. Russian original) Zbl 1336.65065 Cybern. Syst. Anal. 51, No. 6, 978-991 (2015); translation from Kibern. Sist. Anal. 2015, No. 6, 160-173 (2015). MSC: 65F22 PDFBibTeX XMLCite \textit{E. G. Revunova}, Cybern. Syst. Anal. 51, No. 6, 978--991 (2015; Zbl 1336.65065); translation from Kibern. Sist. Anal. 2015, No. 6, 160--173 (2015) Full Text: DOI
Calvetti, Daniela; Somersalo, Erkki; Spies, Ruben Variable order smoothness priors for ill-posed inverse problems. (English) Zbl 1309.65045 Math. Comput. 84, No. 294, 1753-1773 (2015). MSC: 65F22 65C20 PDFBibTeX XMLCite \textit{D. Calvetti} et al., Math. Comput. 84, No. 294, 1753--1773 (2015; Zbl 1309.65045) Full Text: DOI
Gazzola, Silvia; Novati, Paolo; Russo, Maria Rosaria Embedded techniques for choosing the parameter in Tikhonov regularization. (English) Zbl 1340.65068 Numer. Linear Algebra Appl. 21, No. 6, 796-812 (2014). Reviewer: Constantin Popa (Constanţa) MSC: 65F22 65F10 PDFBibTeX XMLCite \textit{S. Gazzola} et al., Numer. Linear Algebra Appl. 21, No. 6, 796--812 (2014; Zbl 1340.65068) Full Text: DOI arXiv
Novati, Paolo; Russo, Maria Rosaria Adaptive Arnoldi-Tikhonov regularization for image restoration. (English) Zbl 1298.65071 Numer. Algorithms 65, No. 4, 745-757 (2014). MSC: 65F22 65D18 94A08 PDFBibTeX XMLCite \textit{P. Novati} and \textit{M. R. Russo}, Numer. Algorithms 65, No. 4, 745--757 (2014; Zbl 1298.65071) Full Text: DOI
Novati, Paolo; Russo, Maria Rosaria A GCV based Arnoldi-Tikhonov regularization method. (English) Zbl 1317.65104 BIT 54, No. 2, 501-521 (2014). Reviewer: Martin Plešinger (Liberec) MSC: 65F22 65F10 PDFBibTeX XMLCite \textit{P. Novati} and \textit{M. R. Russo}, BIT 54, No. 2, 501--521 (2014; Zbl 1317.65104) Full Text: DOI arXiv
Lampe, Jörg; Voss, Heinrich Large-scale dual regularized total least squares. (English) Zbl 1295.65043 ETNA, Electron. Trans. Numer. Anal. 42, 13-40 (2014). MSC: 65F20 65F22 65F10 PDFBibTeX XMLCite \textit{J. Lampe} and \textit{H. Voss}, ETNA, Electron. Trans. Numer. Anal. 42, 13--40 (2014; Zbl 1295.65043) Full Text: EMIS
Rachkovskij, D. A.; Revunova, E. G. A randomized method for solving discrete ill-posed problems. (English. Russian original) Zbl 1311.65043 Cybern. Syst. Anal. 48, No. 4, 621-635 (2012); translation from Kibern. Sist. Anal. No. 4, 163-181 (2012). MSC: 65F22 PDFBibTeX XMLCite \textit{D. A. Rachkovskij} and \textit{E. G. Revunova}, Cybern. Syst. Anal. 48, No. 4, 621--635 (2012; Zbl 1311.65043); translation from Kibern. Sist. Anal. No. 4, 163--181 (2012) Full Text: DOI
Sladek, Jan; Sladek, Vladimir; Wen, Pihua H.; Hon, Benny Inverse heat conduction problems in three-dimensional anisotropic functionally graded solids. (English) Zbl 1259.80011 J. Eng. Math. 75, 157-171 (2012). Reviewer: Viktor Shevchuk (Lviv) MSC: 80A23 65M32 65M60 65M06 80M20 65F22 PDFBibTeX XMLCite \textit{J. Sladek} et al., J. Eng. Math. 75, 157--171 (2012; Zbl 1259.80011) Full Text: DOI
Novati, P.; Redivo-Zaglia, M.; Russo, M. R. Preconditioning linear systems via matrix function evaluation. (English) Zbl 1255.65075 Appl. Numer. Math. 62, No. 12, 1804-1818 (2012). MSC: 65F08 65F22 65R20 65D18 PDFBibTeX XMLCite \textit{P. Novati} et al., Appl. Numer. Math. 62, No. 12, 1804--1818 (2012; Zbl 1255.65075) Full Text: DOI arXiv
Lampe, J.; Voss, H. Efficient determination of the hyperparameter in regularized total least squares problems. (English) Zbl 1246.65063 Appl. Numer. Math. 62, No. 9, 1229-1241 (2012). MSC: 65F20 65F22 PDFBibTeX XMLCite \textit{J. Lampe} and \textit{H. Voss}, Appl. Numer. Math. 62, No. 9, 1229--1241 (2012; Zbl 1246.65063) Full Text: DOI
Guibert, A.; Coulomb, J.-L.; Chadebec, O.; Rannou, C. Inversion improvement of a corrosion diagnosis thanks to an inequality constraint. (English) Zbl 1241.78035 Inverse Probl. Sci. Eng. 20, No. 1, 75-92 (2012). MSC: 78A57 78M50 65F22 65F20 93B30 PDFBibTeX XMLCite \textit{A. Guibert} et al., Inverse Probl. Sci. Eng. 20, No. 1, 75--92 (2012; Zbl 1241.78035) Full Text: DOI HAL
Benoit, J.; Chauvière, C.; Bonnet, P. Source identification in time domain electromagnetics. (English) Zbl 1242.78036 J. Comput. Phys. 231, No. 8, 3446-3456 (2012). MSC: 78M25 78A25 35Q61 35R30 65F20 65F22 PDFBibTeX XMLCite \textit{J. Benoit} et al., J. Comput. Phys. 231, No. 8, 3446--3456 (2012; Zbl 1242.78036) Full Text: DOI
Lampe, Jörg; Reichel, Lothar; Voss, Heinrich Large-scale Tikhonov regularization via reduction by orthogonal projection. (English) Zbl 1241.65044 Linear Algebra Appl. 436, No. 8, 2845-2865 (2012). MSC: 65F22 PDFBibTeX XMLCite \textit{J. Lampe} et al., Linear Algebra Appl. 436, No. 8, 2845--2865 (2012; Zbl 1241.65044) Full Text: DOI
Brezinski, C.; Novati, P.; Redivo-Zaglia, M. A rational Arnoldi approach for ill-conditioned linear systems. (English) Zbl 1254.65051 J. Comput. Appl. Math. 236, No. 8, 2063-2077 (2012). Reviewer: Martin Reißel (Aachen) MSC: 65F22 65F10 65F35 PDFBibTeX XMLCite \textit{C. Brezinski} et al., J. Comput. Appl. Math. 236, No. 8, 2063--2077 (2012; Zbl 1254.65051) Full Text: DOI arXiv
Taylan, Pakize; Weber, Gerhard-Wilhelm; Özkurt, Fatma Yerlikaya A new approach to multivariate adaptive regression splines by using Tikhonov regularization and continuous optimization. (English) Zbl 1208.41007 Top 18, No. 2, 377-395 (2010). Reviewer: Martin D. Buhmann (Gießen) MSC: 41A15 47N10 65F22 62G08 90C51 PDFBibTeX XMLCite \textit{P. Taylan} et al., Top 18, No. 2, 377--395 (2010; Zbl 1208.41007) Full Text: DOI
Marin, Liviu; Munteanu, Ligia Boundary reconstruction in two-dimensional steady state anisotropic heat conduction using a regularized meshless method. (English) Zbl 1255.80016 Int. J. Heat Mass Transfer 53, No. 25-26, 5815-5826 (2010). MSC: 80A23 80M50 65F22 PDFBibTeX XMLCite \textit{L. Marin} and \textit{L. Munteanu}, Int. J. Heat Mass Transfer 53, No. 25--26, 5815--5826 (2010; Zbl 1255.80016) Full Text: DOI
Hoffmann, R. S.; Seewald, A.; Schneider, P. S.; França, F. H. R. Inverse design of thermal systems with spectrally dependent emissivities. (English) Zbl 1183.80098 Int. J. Heat Mass Transfer 53, No. 5-6, 931-939 (2010). MSC: 80A23 80M25 65F22 65F20 PDFBibTeX XMLCite \textit{R. S. Hoffmann} et al., Int. J. Heat Mass Transfer 53, No. 5--6, 931--939 (2010; Zbl 1183.80098) 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
Elfving, Tommy; Skoglund, Ingegerd A direct method for a regularized least-squares problem. (English) Zbl 1224.65106 Numer. Linear Algebra Appl. 16, No. 8, 649-675 (2009). MSC: 65F20 65F22 92D40 PDFBibTeX XMLCite \textit{T. Elfving} and \textit{I. Skoglund}, Numer. Linear Algebra Appl. 16, No. 8, 649--675 (2009; Zbl 1224.65106) Full Text: DOI
Hnětynková, Iveta; Plešinger, Martin; Strakoš, Zdeněk The regularizing effect of the Golub-Kahan iterative bidiagonalization and revealing the noise level in the data. (English) Zbl 1184.65044 BIT 49, No. 4, 669-696 (2009). MSC: 65F22 65F20 15A06 15A21 PDFBibTeX XMLCite \textit{I. Hnětynková} et al., BIT 49, No. 4, 669--696 (2009; Zbl 1184.65044) Full Text: DOI
Cartis, C.; Gould, N. I. M.; Toint, P. L. Trust-region and other regularisations of linear least-squares problems. (English) Zbl 1165.65019 BIT 49, No. 1, 21-53 (2009). Reviewer: Constantin Popa (Constanţa) MSC: 65F20 65F22 65K05 90C25 90C51 PDFBibTeX XMLCite \textit{C. Cartis} et al., BIT 49, No. 1, 21--53 (2009; Zbl 1165.65019) Full Text: DOI Link
Brezinski, C.; Rodriguez, G.; Seatzu, S. Error estimates for linear systems with applications to regularization. (English) Zbl 1162.65018 Numer. Algorithms 49, No. 1-4, 85-104 (2008). MSC: 65F22 65F10 PDFBibTeX XMLCite \textit{C. Brezinski} et al., Numer. Algorithms 49, No. 1--4, 85--104 (2008; Zbl 1162.65018) Full Text: DOI
Lampe, J.; Voss, H. On a quadratic eigenproblem occurring in regularized total least squares. (English) Zbl 1393.15013 Comput. Stat. Data Anal. 52, No. 2, 1090-1102 (2007). MSC: 15A18 65F15 65F20 65F22 PDFBibTeX XMLCite \textit{J. Lampe} and \textit{H. Voss}, Comput. Stat. Data Anal. 52, No. 2, 1090--1102 (2007; Zbl 1393.15013) Full Text: DOI
Hansen, Per Christian; Jensen, Toke Koldborg; Rodriguez, Giuseppe An adaptive pruning algorithm for the discrete L-curve criterion. (English) Zbl 1101.65044 J. Comput. Appl. Math. 198, No. 2, 483-492 (2007). MSC: 65F22 65F20 PDFBibTeX XMLCite \textit{P. C. Hansen} et al., J. Comput. Appl. Math. 198, No. 2, 483--492 (2007; Zbl 1101.65044) Full Text: DOI
Bunse-Gerstner, Angelika; Guerra-Ones, Valia; De La Vega, Humberto Madrid An improved preconditioned LSQR for discrete ill-posed problems. (English) Zbl 1104.65034 Math. Comput. Simul. 73, No. 1-4, 65-75 (2006). MSC: 65F22 65F20 65F35 PDFBibTeX XMLCite \textit{A. Bunse-Gerstner} et al., Math. Comput. Simul. 73, No. 1--4, 65--75 (2006; Zbl 1104.65034) Full Text: DOI
Mastronardi, N.; Lemmerling, P.; Van Huffel, S. Fast regularized structured total least squares algorithm for solving the basic deconvolution problem. (English) Zbl 1164.65374 Numer. Linear Algebra Appl. 12, No. 2-3, 201-209 (2005). Reviewer: Jan Chleboun (Praha) MSC: 65F20 62P10 65F22 PDFBibTeX XMLCite \textit{N. Mastronardi} et al., Numer. Linear Algebra Appl. 12, No. 2--3, 201--209 (2005; Zbl 1164.65374) Full Text: DOI
Marin, L. A meshless method for solving the Cauchy problem in three-dimensional elastostatics. (English) Zbl 1127.74014 Comput. Math. Appl. 50, No. 1-2, 73-92 (2005). MSC: 74G15 65F22 65N22 74B05 PDFBibTeX XMLCite \textit{L. Marin}, Comput. Math. Appl. 50, No. 1--2, 73--92 (2005; Zbl 1127.74014) Full Text: DOI
Fierro, Ricardo D.; Hansen, Per Christian UTV Expansin pack: Special-purpose rank-revealing algorithms. (English) Zbl 1079.65026 Numer. Algorithms 40, No. 1, 47-66 (2005). MSC: 65F05 65Y15 15-04 65F25 PDFBibTeX XMLCite \textit{R. D. Fierro} and \textit{P. C. Hansen}, Numer. Algorithms 40, No. 1, 47--66 (2005; Zbl 1079.65026) Full Text: DOI
Eldén, L.; Hansen, P. C.; Rojas, M. Minimization of linear functionals defined on solutions of large-scale discrete ill-posed problems. (English) Zbl 1084.65035 BIT 45, No. 2, 329-340 (2005). Reviewer: R. P. Tewarson (Stony Brook) MSC: 65F22 65F20 PDFBibTeX XMLCite \textit{L. Eldén} et al., BIT 45, No. 2, 329--340 (2005; Zbl 1084.65035) Full Text: DOI
Mastronardi, N.; Lemmerling, P.; Kalsi, A.; O’Leary, D. P.; Van Huffel, S. Implementation of the regularized structured total least squares algorithms for blind image deblurring. (English) Zbl 1060.94502 Linear Algebra Appl. 391, 203-221 (2004). MSC: 94A08 68U10 65F22 65F30 15A23 PDFBibTeX XMLCite \textit{N. Mastronardi} et al., Linear Algebra Appl. 391, 203--221 (2004; Zbl 1060.94502) Full Text: DOI
Volokh, K. Yu.; Vilnay, O. Pin-pointing solution of ill-conditioned square systems of linear equations. (English) Zbl 0955.65031 Appl. Math. Lett. 13, No. 7, 119-124 (2000). MSC: 65F22 65F05 PDFBibTeX XMLCite \textit{K. Yu. Volokh} and \textit{O. Vilnay}, Appl. Math. Lett. 13, No. 7, 119--124 (2000; Zbl 0955.65031) Full Text: DOI
Fierro, Ricardo D.; Hansen, Per Christian; Hansen, Peter Søren Kirk UTV tools: Matlab templates for rank-revealing UTV decompositions. (English) Zbl 0936.65054 Numer. Algorithms 20, No. 2-3, 165-194 (1999). Reviewer: F.Szidarovszky (Tucson) MSC: 65F25 65F20 65Y15 PDFBibTeX XMLCite \textit{R. D. Fierro} et al., Numer. Algorithms 20, No. 2--3, 165--194 (1999; Zbl 0936.65054) Full Text: DOI
Hansen, Per Christian Rank-deficient and discrete ill-posed problems. Numerical aspects of linear inversion. (English) Zbl 0890.65037 SIAM Monographs on Mathematical Modeling and Computation, 4. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. 247 p. (1997). Reviewer: C.W.Groetsch (Cincinnati) MSC: 65F20 65J20 47A50 15A09 65R30 45B05 65-02 PDFBibTeX XMLCite \textit{P. C. Hansen}, Rank-deficient and discrete ill-posed problems. Numerical aspects of linear inversion. Philadelphia, PA: SIAM (1997; Zbl 0890.65037) Full Text: DOI
Fierro, Ricardo D.; Hansen, Per Christian Low-rank revealing \(UTV\) decompositions. (English) Zbl 0887.65043 Numer. Algorithms 15, No. 1, 37-55 (1997). Reviewer: Liu Xinguo (Qingdao) MSC: 65F25 PDFBibTeX XMLCite \textit{R. D. Fierro} and \textit{P. C. Hansen}, Numer. Algorithms 15, No. 1, 37--55 (1997; Zbl 0887.65043) Full Text: DOI