Herman, Elizabeth; Alexanderian, Alen; Saibaba, Arvind K. Randomization and reweighted \(\ell_1\)-minimization for A-optimal design of linear inverse problems. (English) Zbl 1442.62175 SIAM J. Sci. Comput. 42, No. 3, A1714-A1740 (2020). MSC: 62K05 62-08 62F15 35Q62 35R30 68W20 PDF BibTeX XML Cite \textit{E. Herman} et al., SIAM J. Sci. Comput. 42, No. 3, A1714--A1740 (2020; Zbl 1442.62175) Full Text: DOI
Geiping, Jonas; Moeller, Michael Composite optimization by nonconvex majorization-minimization. (English) Zbl 1419.90089 SIAM J. Imaging Sci. 11, No. 4, 2494-2528 (2018). MSC: 90C26 90C06 68U10 32B20 65K10 47J06 PDF BibTeX XML Cite \textit{J. Geiping} and \textit{M. Moeller}, SIAM J. Imaging Sci. 11, No. 4, 2494--2528 (2018; Zbl 1419.90089) Full Text: DOI arXiv
Alexanderian, Alen; Saibaba, Arvind K. Efficient D-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems. (English) Zbl 1401.62123 SIAM J. Sci. Comput. 40, No. 5, A2956-A2985 (2018). MSC: 62K05 62F15 35Q62 65C60 PDF BibTeX XML Cite \textit{A. Alexanderian} and \textit{A. K. Saibaba}, SIAM J. Sci. Comput. 40, No. 5, A2956--A2985 (2018; Zbl 1401.62123) Full Text: DOI arXiv
Bellis, Cédric; Trabelsi, Manel; Frémy, Flavien Reconstructing material properties by deconvolution of full-field measurement images: the conductivity case. (English) Zbl 1367.65157 Inverse Probl. 33, No. 3, Article ID 035012, 19 p. (2017). Reviewer: Sarah Eberle (Tübingen) MSC: 65N21 35Q60 35R25 35R30 65T60 65N30 PDF BibTeX XML Cite \textit{C. Bellis} et al., Inverse Probl. 33, No. 3, Article ID 035012, 19 p. (2017; Zbl 1367.65157) Full Text: DOI
Leitão, A.; Svaiter, B. F. On projective Landweber-Kaczmarz methods for solving systems of nonlinear ill-posed equations. (English) Zbl 1344.65052 Inverse Probl. 32, No. 2, Article ID 025004, 20 p. (2016). Reviewer: Zhen Mei (Toronto) MSC: 65J15 47J25 65J20 47J06 PDF BibTeX XML Cite \textit{A. Leitão} and \textit{B. F. Svaiter}, Inverse Probl. 32, No. 2, Article ID 025004, 20 p. (2016; Zbl 1344.65052) Full Text: DOI
Xiang, Hua; Zou, Jun Randomized algorithms for large-scale inverse problems with general Tikhonov regularizations. (English) Zbl 1327.65077 Inverse Probl. 31, No. 8, Article ID 085008, 24 p. (2015). MSC: 65F22 65F20 68W20 PDF BibTeX XML Cite \textit{H. Xiang} and \textit{J. Zou}, Inverse Probl. 31, No. 8, Article ID 085008, 24 p. (2015; Zbl 1327.65077) Full Text: DOI arXiv
Lv, Xiao-Guang; Huang, Ting-Zhu; Jiang, Le; Liu, Jun Two global iterative methods for ill-posed problems from image restoration. (English) Zbl 1320.65036 J. Comput. Anal. Appl. 18, No. 2, 219-237 (2015). MSC: 65D18 94A08 65F22 PDF BibTeX XML Cite \textit{X.-G. Lv} et al., J. Comput. Anal. Appl. 18, No. 2, 219--237 (2015; Zbl 1320.65036)
Ochs, Peter; Dosovitskiy, Alexey; Brox, Thomas; Pock, Thomas On iteratively reweighted algorithms for nonsmooth nonconvex optimization in computer vision. (English) Zbl 1326.65078 SIAM J. Imaging Sci. 8, No. 1, 331-372 (2015). MSC: 65K10 90C30 94A08 90C06 47J06 49J52 62H35 PDF BibTeX XML Cite \textit{P. Ochs} et al., SIAM J. Imaging Sci. 8, No. 1, 331--372 (2015; Zbl 1326.65078) 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 PDF BibTeX XML Cite \textit{M. E. Hochstenbach} et al., J. Comput. Appl. Math. 273, 132--149 (2015; Zbl 1295.65046) Full Text: DOI
Viloche Bazán, Fermín S.; Cunha, Maria C. C.; Borges, Leonardo S. Extension of GKB-FP algorithm to large-scale general-form Tikhonov regularization. (English) Zbl 1340.65071 Numer. Linear Algebra Appl. 21, No. 3, 316-339 (2014). MSC: 65F22 65F35 65F08 PDF BibTeX XML Cite \textit{F. S. Viloche Bazán} et al., Numer. Linear Algebra Appl. 21, No. 3, 316--339 (2014; Zbl 1340.65071) Full Text: DOI
Kalmikov, Alexander G.; Heimbach, Patrick A Hessian-based method for uncertainty quantification in global Ocean state estimation. (English) Zbl 1311.35321 SIAM J. Sci. Comput. 36, No. 5, S267-S295 (2014). Reviewer: Vladimir Mityushev (Kraków) MSC: 35Q86 86A05 62J02 62J10 65C60 65M15 62P12 68N99 65M32 86A22 PDF BibTeX XML Cite \textit{A. G. Kalmikov} and \textit{P. Heimbach}, SIAM J. Sci. Comput. 36, No. 5, S267--S295 (2014; Zbl 1311.35321) Full Text: DOI
Geng, Jian; Navon, I. Michael; Chen, Xiao Non-parametric calibration of the local volatility surface for European options using a second-order Tikhonov regularization. (English) Zbl 1294.91187 Quant. Finance 14, No. 1, 73-85 (2014). MSC: 91G60 91G20 65F22 65M30 PDF BibTeX XML Cite \textit{J. Geng} et al., Quant. Finance 14, No. 1, 73--85 (2014; Zbl 1294.91187) Full Text: DOI
Arridge, S. R.; Betcke, M. M.; Harhanen, L. Iterated preconditioned LSQR method for inverse problems on unstructured grids. (English) Zbl 1321.65094 Inverse Probl. 30, No. 7, Article ID 075009, 27 p. (2014). MSC: 65K05 90C20 65F22 90C06 65F08 PDF BibTeX XML Cite \textit{S. R. Arridge} et al., Inverse Probl. 30, No. 7, Article ID 075009, 27 p. (2014; Zbl 1321.65094) Full Text: DOI
Wang, Qian; Dai, Hua A regularizing GMERR method for solving discrete ill-posed problems. (Chinese. English summary) Zbl 1299.65070 Math. Numer. Sin. 35, No. 2, 195-204 (2013). MSC: 65F22 65F10 PDF BibTeX XML Cite \textit{Q. Wang} and \textit{H. Dai}, Math. Numer. Sin. 35, No. 2, 195--204 (2013; Zbl 1299.65070)
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 PDF BibTeX XML Cite \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 PDF BibTeX XML Cite \textit{D. R. Martin} and \textit{L. Reichel}, BIT 53, No. 1, 153--173 (2013; Zbl 1262.65053) Full Text: DOI
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. (English) Zbl 1293.65061 Appl. Math. Comput. 219, No. 4, 2100-2113 (2012). MSC: 65F20 65F22 PDF BibTeX XML Cite \textit{F. S. Viloche Bazán} et al., Appl. Math. Comput. 219, No. 4, 2100--2113 (2012; Zbl 1293.65061) Full Text: DOI
Viloche Bazán, Fermín S.; Borges, Leonardo S. GKB-FP: An algorithm for large-scale discrete ill-posed problems. (English) Zbl 1207.65039 BIT 50, No. 3, 481-507 (2010). Reviewer: Raffaella Pavani (Milano) MSC: 65F20 PDF BibTeX XML Cite \textit{F. S. Viloche Bazán} and \textit{L. S. Borges}, BIT 50, No. 3, 481--507 (2010; Zbl 1207.65039) Full Text: DOI
Landi, G.; Loli Piccolomini, E. A fast projected quasi-Newton method for nonnegative Tikhonov regularization. (English) Zbl 1157.65035 Int. J. Math. Comput. Sci. 3, No. 3, 199-213 (2008). MSC: 65K05 90C20 90C53 94A08 PDF BibTeX XML Cite \textit{G. Landi} and \textit{E. Loli Piccolomini}, Int. J. Math. Comput. Sci. 3, No. 3, 199--213 (2008; Zbl 1157.65035)
Haber, E.; Horesh, L.; Tenorio, L. Numerical methods for experimental design of large-scale linear ill-posed inverse problems. (English) Zbl 1153.65062 Inverse Probl. 24, No. 5, Article ID 055012, 17 p. (2008). MSC: 65K05 62K05 65C60 90C15 90C06 PDF BibTeX XML Cite \textit{E. Haber} et al., Inverse Probl. 24, No. 5, Article ID 055012, 17 p. (2008; Zbl 1153.65062) Full Text: DOI
Morigi, S.; Reichel, L.; Sgallari, F.; Zama, F. An iterative method for linear discrete ill-posed problems with box constraints. (English) Zbl 1101.65045 J. Comput. Appl. Math. 198, No. 2, 505-520 (2007). MSC: 65F22 65F10 45B05 65R20 65R30 PDF BibTeX XML Cite \textit{S. Morigi} et al., J. Comput. Appl. Math. 198, No. 2, 505--520 (2007; Zbl 1101.65045) Full Text: DOI
Morigi, S.; Reichel, L.; Sgallari, F.; Zama, F. Iterative methods for ill-posed problems and semiconvergent sequences. (English) Zbl 1092.65025 J. Comput. Appl. Math. 193, No. 1, 157-167 (2006). MSC: 65F10 65F22 PDF BibTeX XML Cite \textit{S. Morigi} et al., J. Comput. Appl. Math. 193, No. 1, 157--167 (2006; Zbl 1092.65025) Full Text: DOI
Calvetti, D.; Reichel, L.; Shuibi, A. L-curve and curvature bounds for Tikhonov regularization. (English) Zbl 1049.65029 Numer. Algorithms 35, No. 2-4, 301-314 (2004). MSC: 65F22 65F10 PDF BibTeX XML Cite \textit{D. Calvetti} et al., Numer. Algorithms 35, No. 2--4, 301--314 (2004; Zbl 1049.65029) Full Text: DOI
Antontsev, S. N.; Gagneux, Gérard; Vallet, Guy Some stratigraphic control problems. (Russian) Zbl 1038.76039 Prikl. Mekh. Tekh. Fiz. 44, No. 6, 85-94 (2003); translation in J. Appl. Mech. Tech. Phys. 44, No. 6, 821-828 (2003). Reviewer: N. I. Alexandrova (Novosibirsk) MSC: 76N25 76R50 76N10 35Q35 PDF BibTeX XML Cite \textit{S. N. Antontsev} et al., Prikl. Mekh. Tekh. Fiz. 44, No. 6, 85--94 (2003; Zbl 1038.76039); translation in J. Appl. Mech. Tech. Phys. 44, No. 6, 821--828 (2003)
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 PDF BibTeX XML Cite \textit{D. Calvetti} and \textit{L. Reichel}, BIT 43, No. 2, 263--283 (2003; Zbl 1038.65048) Full Text: DOI
Mc Carthy, P. J. Direct analytic model of the L-curve for Tikhonov regularization parameter selection. (English) Zbl 1027.65049 Inverse Probl. 19, No. 3, 643-663 (2003). MSC: 65F22 65F20 PDF BibTeX XML Cite \textit{P. J. Mc Carthy}, Inverse Probl. 19, No. 3, 643--663 (2003; Zbl 1027.65049) Full Text: DOI
Wang, Yanfei; Yuan, Yaxiang; Zhang, Hongchao A trust region-CG algorithm for deblurring problem in atmospheric image reconstruction. (English) Zbl 1100.65502 Sci. China, Ser. A 45, No. 6, 731-740 (2002). MSC: 65J10 65K10 65J20 47A52 65K05 90C51 94A08 PDF BibTeX XML Cite \textit{Y. Wang} et al., Sci. China, Ser. A 45, No. 6, 731--740 (2002; Zbl 1100.65502)
Rojas, Marielba; Sorensen, Danny C. A trust-region approach to the regularization of large-scale discrete forms of ill-posed problems. (English) Zbl 1006.86004 SIAM J. Sci. Comput. 23, No. 6, 1842-1860 (2002). MSC: 86A22 65K10 90C06 PDF BibTeX XML Cite \textit{M. Rojas} and \textit{D. C. Sorensen}, SIAM J. Sci. Comput. 23, No. 6, 1842--1860 (2002; Zbl 1006.86004) Full Text: DOI
Pereyra, V. Asynchronous distributed solution of large scale nonlinear inversion problems. (English) Zbl 0932.65067 Appl. Numer. Math. 30, No. 1, 31-40 (1999). Reviewer: Yu Wenhuan (Tianjin) MSC: 65K05 90C30 86A15 86A22 PDF BibTeX XML Cite \textit{V. Pereyra}, Appl. Numer. Math. 30, No. 1, 31--40 (1999; Zbl 0932.65067) Full Text: DOI
Golub, Gene H.; von Matt, Urs Generalized cross-validation for large scale problems. (English) Zbl 0878.65032 Van Huffel, Sabine (ed.), Recent advances in total least squares techniques and errors-in-variables modeling. Proceedings of the 2nd international workshop on total least squares and errors-in-variables modeling, Leuven, Belgium, August 21-24, 1996. Philadelphia, PA: Society for Industrial and Applied Mathematics, SIAM. 139-148 (1997). MSC: 65F20 PDF BibTeX XML Cite \textit{G. H. Golub} and \textit{U. von Matt}, in: Recent advances in total least squares techniques and errors-in-variables modeling. Proceedings of the 2nd international workshop on total least squares and errors-in-variables modeling, Leuven, Belgium, August 21-24, 1996. Philadelphia, PA: Society for Industrial and Applied Mathematics, SIAM. 139--148 (1997; Zbl 0878.65032)
Plemmons, Robert J. Some applications of iterative deconvolution. (English) Zbl 0860.65134 Southeast Asian Bull. Math. 20, No. 3, 23-32 (1996). MSC: 65R20 65-02 65F10 60G35 45E10 65R30 65C99 PDF BibTeX XML Cite \textit{R. J. Plemmons}, Southeast Asian Bull. Math. 20, No. 3, 23--32 (1996; Zbl 0860.65134)
Sevink, Agur G. J.; Herman, Gérard C. Three-dimensional, nonlinear, asymptotic seismic inversion. (English) Zbl 0858.65129 Inverse Probl. 12, No. 5, 757-777 (1996). Reviewer: V.Pereyra (Los Altos) MSC: 65R20 65R30 45B05 86A15 86A22 PDF BibTeX XML Cite \textit{A. G. J. Sevink} and \textit{G. C. Herman}, Inverse Probl. 12, No. 5, 757--777 (1996; Zbl 0858.65129) Full Text: DOI
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 PDF BibTeX XML Cite \textit{Å. Björck} et al., BIT 34, No. 4, 510--534 (1994; Zbl 0821.65023) Full Text: DOI
Oldenburg, Douglas W.; Li, Yaoguo Subspace linear inverse method. (English) Zbl 0815.65072 Inverse Probl. 10, No. 4, 915-935 (1994). Reviewer: B.Hofmann (Chemnitz) MSC: 65J10 65J20 86A60 47A50 PDF BibTeX XML Cite \textit{D. W. Oldenburg} and \textit{Y. Li}, Inverse Probl. 10, No. 4, 915--935 (1994; Zbl 0815.65072) Full Text: DOI
Dikoussar, Vassili V. Continuation methods in boundary value problems. (English) Zbl 0794.65061 Bulirsch, R. (ed.) et al., Computational optimal control. Proceedings of the 9th IFAC workshop on control applications of optimization held at the Fachhochschule München in September 1992. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 115, 65-70 (1994). MSC: 65K10 93B40 65L10 34B15 93C15 93A15 PDF BibTeX XML Cite \textit{V. V. Dikoussar}, ISNM, Int. Ser. Numer. Math. 115, 65--70 (1994; Zbl 0794.65061)
Hanke, Martin; Nagy, James; Plemmons, Robert Preconditioned iterative regularization for ill-posed problems. (English) Zbl 0794.65039 Reichel, Lothar (ed.) et al., Numerical linear algebra. Proceedings of the conference in numerical linear algebra and scientific computation, Kent, OH, USA, March 13-14, 1992. Berlin: Walter de Gruyter. 141-163 (1993). MSC: 65F20 65J10 65R30 65J20 65R20 PDF BibTeX XML Cite \textit{M. Hanke} et al., in: Numerical linear algebra. Proceedings of the conference in numerical linear algebra and scientific computation, Kent, OH, USA, March 13-14, 1992. Berlin: Walter de Gruyter. 141--163 (1993; Zbl 0794.65039)
Hanke, Martin; Hansen, Per Christian Regularization methods for large-scale problems. (English) Zbl 0805.65058 Surv. Math. Ind. 3, No. 4, 253-315 (1993). Reviewer: C.W.Groetsch (Cincinnati) MSC: 65J20 65F20 65-02 65J10 65R20 65R30 47A50 PDF BibTeX XML Cite \textit{M. Hanke} and \textit{P. C. Hansen}, Surv. Math. Ind. 3, No. 4, 253--315 (1993; Zbl 0805.65058)
Zenios, Stavros A.; Censor, Yair Parallel computing with block-iterative image reconstruction algorithms. (English) Zbl 0727.65118 Appl. Numer. Math. 7, No. 5, 399-415 (1991). Reviewer: K.Schittkowski (Bayreuth) MSC: 65R10 65R30 65Y05 65K05 90C90 94A12 92C55 90C06 44A12 PDF BibTeX XML Cite \textit{S. A. Zenios} and \textit{Y. Censor}, Appl. Numer. Math. 7, No. 5, 399--415 (1991; Zbl 0727.65118) Full Text: DOI
Poggio, T.; Koch, C. Ill-posed problems in early vision: from computational theory to analogue networks. (English) Zbl 0587.65086 Proc. R. Soc. Lond., Ser. A 402, 401 (1985). Reviewer: N.Köckler MSC: 65Z05 35R25 68U20 90C35 49S05 78A10 PDF BibTeX XML Cite \textit{T. Poggio} and \textit{C. Koch}, Proc. R. Soc. Lond., Ser. A 402, 401 (1985; Zbl 0587.65086) Full Text: DOI
Poggio, T.; Koch, C. Ill-posed problems in early vision: from computational theory to analogue networks. (English) Zbl 0587.65085 Proc. R. Soc. Lond., Ser. B 226, 303-323 (1985). Reviewer: N.Köckler MSC: 65Z05 68U20 90C35 49S05 78A10 35R25 PDF BibTeX XML Cite \textit{T. Poggio} and \textit{C. Koch}, Proc. R. Soc. Lond., Ser. B 226, 303--323 (1985; Zbl 0587.65085) Full Text: DOI