Bibliography on the Kaczmarz Method the Original Paper of Kaczmarz

Bibliography on the Kaczmarz Method the Original Paper of Kaczmarz

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. Meidani, A recursive data-driven model for traffi c flow predictions for locations with faulty sensors, 21st International Conference on Intelligent Transportation Systems (ITSC), Maui, Hawaii, USA, November 4-7, 2018. [14] A. Aleyner, Iterative Methods for Solving Convex Feasibility Problems, Ph.D. Thesis, The Technion — Israel Institute of Technology, Haifa, Israel, 2008. [15] A. Aleyner, S. Reich, Block-iterative algorithms for solving convex feasibility problems in Hilbert and in Banach spaces, Journal of Mathematical Analysis and Applications, 343 (2008) 427-435. 1 [16] S. Al-Homidan, Semidefinite and second-order cone optimization approach for the Toeplitz matrix approximation problem, J. Numer. Math., 14 (2006) 1—15. [17] Z. Allen-Zhu, Z. Qu, P. Richtárik, Y. Yuan, Even faster accelerated coordinate descent using non-uniform sampling, Proceedings of the 33rd International Conference on Machine Learning, New York, NY, USA, 2016. JMLR: W&CP volume 48. [18] M.A.M. 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. Tam, The Douglas-Rachford algorithm for convex and nonconvex feasibility problems, arXiv:1904.09148v1, 2019. [41] K. Arunachalam, L. Udpa, S.S. Udpa, MEMS based computed tomographic scanner for border security, IEEE International Conference on Electro Information Technology, Lincoln, NE, 22-25 May 2005 (5 pp). [42] K. Arunachalam, S.S. Udpa, L. Udpa, An X-ray security screening technique with limited field-of-view, International Journal of Applied Electromagnetics and Mechanics, 24 (2006) 79-89. [43] K. Arunachalam, S.S. Udpa, L. Udpa, Tomographic imaging for border security applications, International Journal of Applied Electromagnetics and Mechanics, 25 (2007) 389-394. [44] G. Asova, Tomography of the Electron Beam Transverse Phase Space at PITZ, Ph.D. Thesis, Sofia, Bulgaria, 2012. [45] A. N. Astafyev, S.I. Gerashchenko, M.V. Markuleva and M.S. 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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