January, 23rd, 2021 Andrzej Cegielski Institute of Mathematics University of Zielona Góra ul. Szafrana 4a, 65-516 Zielona Góra, Poland e-mail: [email protected] Bibliography on the Kaczmarz method The original paper of Kaczmarz [Kac37] S. Kaczmarz, Angenäherte Auflösung von Systemen linearer Gleichungen (Przyblizone· rozwi ¾azywanie uk÷adówrówna´n liniowych), Bull. Intern. Acad. Polonaise Sci. Lett., Cl. Sci. Math. Nat. A, 35 (1937) 355-357. English translation: S. Kaczmarz, Approximate solution of systems of linear equations, International Journal of Control, 57 (1993) 1269-1271. Publications which cite [Kac37] [1] J. Abaffy, E. Spedicato, A generalization of Huang’smethod for solving systems of linear algebraic equations, Bolletino dell’UnioneMatematica Italiana, 3B (1984) 517-529. [2] J. Abaffy, E. Spedicato, ABS Projection Algorithms: Mathematical Techniques for Linear and Nonlinear Equations, Halstead Press, Chichester UK, 1989. [3] M.I.K. Abir, Iterative CT Reconstruction from Few Projections for the Nondestructive Post Irradiation Examination of Nuclear Fuel Assemblies, Ph.D. Thesis, Missouri University of Science and Technology, Rolla, Missouri, USA, 2015. [4] A. Aboud, A Dualized Kaczmarz Algorithm in Hilbert and Banach Space, Ph.D. Thesis, Iowa State University, Ames, Iowa, USA, 2019. [5] M.F. Adams, A low memory, highly concurrent multigrid algorithm, arXiv:1207.6720v3 (2012). [6] M. Aftanas, Through Wall Imaging with UWB Radar System, Ph.D. Thesis, Technical University of Koice, Koice, Slovakia, 2009. [7] A. Agaskar, Problems in Signal Processing and Inference on Graphs, Ph.D. Thesis, Harvard University, Cambridge, MA, USA, 2015. [8] A. Agaskar, C. Wang, Y.M. Lu, Randomized Kaczmarz algorithms: Exact MSE analysis and optimal sampling probabilities, 2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP), Atlanta, GA, 3-5 Dec. 2014, pp. 389-393. [9] H.K. Aggarwal, A. Majumdar, Extension of sparse randomized Kaczmarz algorithm for multiple measurement vectors, 22nd International Conference on Pattern Recognition, Stockholm, 2014, pp. 1014-1019, doi: 10.1109/ICPR.2014.184. [10] R. Aharoni, P. Duchet, B. Wajnryb, Successive projections on hyperplanes, Journal of Mathematical Analysis and Appli- cations, 103 (1984) 134-138. [11] N.H.F. Al-anbari, M.H.A. Al-Hayani, Evaluation performance of iterative algorithms for 3D image reconstruction in cone beam geometry, Al-Nahrain Journal for Engineering Sciences, 20 (2017) 149-157. [12] Y. Alber, D. Butnariu, Convergence of Bregman projection methods for solving consistent convex feasibility problems in reflexive Banach spaces, Journal of Optimization Theory and Applications, 92 (1997) 33-61. [13] N. Alemazkoor, S. Wang, H. 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Althomali, Towards Ultrasound Computed Tomography Assessment of Bone, Ph.D. Thesis, Queensland University of Technology, Australia, 2018. [19] M.A.M. Althomali, M.-L. Wille, M.P. Shortell, C.M. Langton, Estimation of mechanical stiffness by finite element analysis of ultrasound computed tomography (UCT-FEA); a comparison with X-ray CT based FEA in cancellous bone replica models, Applied Acoustics 133 (2018) 8—15. [20] O.T. Altinoz, A.E. Yilmaz, G. Ciuprina, Use of Kaczmarz’smethod in intelligent-particle swarm optimization, 8th Inter- national Conference on Electrical and Electronics Engineering, Bursa, 28-30 Nov. 2013, pp. 526-530. [21] M. Altman, On the approximate solution of linear algebraic equations, Bulletin de L’Académie Polonaise des Sciences Cl. III, 5 (1957) 365-370. [22] M. Aly, G. Zang, W. Heidrich, P. Wonka, TRex: A tomography reconstruction proximal framework for robust sparse view X-ray applications, arXiv:1606.03601v1 (2016). [23] P.E. An, C.J. Harris, An intelligent driver warning system for vehicle collision avoidance, IEEE Transactions on Systems Man and Cybernetics – Part A: Systems and Humans, 26 (1996) 254-261. [24] P.E. An, M. Brown, C.J. Harris, On the convergence rate performance of the normalized least-mean-square adaptation, IEEE Transactions on Neutral Networks, 8 (1997) 1211-1214. [25] A.H. Andersen, Tomography transform and inverse in geometrical optics, J. Opt. Soc. Am. A, 4 (1987) 1385-1395. [26] A.H. Andersen, A ray tracing approach to restoration and resolution enhancement in experimental ultrasound tomography, Ultrasonic Imaging, 12 (1990) 268-291. [27] M.S. Andersen, P.C. Hansen, Generalized row-action methods for tomographic imaging, Numer. Algor., 67 (2014) 121-144. [28] A.H. Andersen, A.C. Kak, Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm, Ultrasonic Imaging, 6 (1984) 81-94. [29] T. Angsuwatanakul, T. Chanwimalueang, C. Pintavirooj, M. Sangworasil, P.Lertprasert, Improved-resolution X-ray array detector applied for SART fanbeam, International Symposium on Communications and Information Technologies, Bangkok, Oct. 18 —Sept. 20, 2006 , 1145-1148. [30] C.F. Ansley, R. Kohn, Convergence of the backfitting algorithm for additive models, J. Austral. Math. Soc. (Series A), 57 (1994) 316-329. [31] R. Ansorge, Connections between the Cimmino-method and the Kaczmarz-method for the solution of singular and regular systems of equations, Computing 33 (1984) 367-375. [32] A.E. Anuta jr, The mode shape reversal, Computers & Structures, 33 (1989) 103-116. [33] G. Appleby, D.C. Smolarski, A linear acceleration row action method for projecting onto subspaces, Electronic Transactions on Numerical Analysis, 20 (2005) 253-275. [34] F.O. Araujo, Método de Projeções Ortogonais, Ph.D. Thesis, Universidade Federal do Rio Grande do Norte, Natal, Brazil, 2012. [35] A. Aravkin, M.P. Friedlander, F.J. Herrmann, T. van Leeuwen, Robust inversion, dimensionality reduction, and randomized sampling, Mathematical Programming Series B, 134 (2012), 101-125. [36] F. Arcadu, M. Stampanoni, F. Marone, On the crucial impact of the coupling projector-backprojector in iterative tomo- graphic reconstruction, arXiv:1612.05515v1 (2016). [37] R. Arefidamghani, R. Behling, Y. Bello-Cruz, A.N. Iusem and L.-R. Santos, The circumcentered-reflectionmethod achieves better rates than alternating projections, arXiv:2007.14466v1 (2020). 2 [38] F.M. Arrabal-Campos, L.M. Aguilera-Sáez, I. Fernández, Algebraic reconstruction technique for diffusion NMR experi- ments. application to the molecular weight prediction of polymers, J. Phys. Chem. A, 123 (2019) 943—950. [39] S. R. Arridge, J.C. Schotland, Optical tomography: forward and inverse problems, Inverse Problems, 25 (2009) 123010. [40] F.J.A. Artacho, R. Campoy, M.K. 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Gerashchenko, Neural Network System for Medical Data Approximation, 2020 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering, DOI: 10.1109/EIConRus49466.2020.9039353 [46] K.J. Åstrom, Theory and applications of adaptive control —a survey, Automatica, 19 (1983) 471-486. [47] K.J. Åström, P. Eykhoff, System identification —a survey, Automatica, 7 (1971) 123-162. [48] E. Atkinson and M. Carbin, Programming and reasoning with partial observability, Proc. ACM Program. Lang., 4 (2020), No. OOPSLA, Article 200. [49] A. Autret, Amélioration qualitative et quantitative de reconstruction TEP sur plate-forme graphique, Ph.D. Thesis, Uni- versité Européenne de Bretagne, France, 2015. [50] E. Aved’yan, Learning systems, Springer, London, 1995. [51] E. Aved’yan, Deterministic algorithms, in: E. Aved’yan Learning systems, Springer, London, 1995, pp. 16-39. [52] E. Aved’yan, The cerebellar model articulation controller (CMAC), in: E. 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