Projection Algorithms: Stefan Kaczmarz 125th Birthday Anniversary

31.08.2020 - 05.09.2020 | Będlewo

Projection Algorithms: Stefan Kaczmarz 125th birthday anniversary, Będlewo, Poland, August 31st - –September 5th, 2020

  Conference place



Aim and Scope

In 1937 Stefan Kaczmarz (1895-1939) discovered an iterative algorithm for solving a system of linear equations [Kac37], known as Kaczmarz’s algorithm or Kaczmarz’s method. The result remained almost unnoticed for over 30 years until the 70th of the 20th century, when it turned out that the method could have a lot of applications in various areas of mathematics as well as many practical application in physics, in medicine and in technical sciences, e.g., in the computerized tomography and in many other imaging technologies [Byr08, CZ98, Deu92, Her09, SY98]. In the past 3 decades the method has been developed signi…cantly and has been embedded in a broad class of projection algorithms [BB96, BBL97, BC11, Bre97, Ceg12, CC15, CZ18]. Since that time Kaczmarz’s short 3-page paper [Kac37] has been cited in over 1000 publications, most of them were published in the past 20 years. A comprehensive bibliography on Kaczmarz’s method can be found on the site.

For the researchers who work in the area of projection methods and their applications in mathematics, the conference is an occasion to meet and to talk. The researchers who work on applications of Kaczmarz’s method and projection methods in physics, medicine and in technical sciences are also welcome. The aim of the conference is to present the state of art of these methods and their applications, to present open questions, to give a possibility of a fruitful cooperation among researchers working in various areas. There will also be a possibility to present results which are related to other publications of Stefan Kaczmarz. On the occasion of Stefan Kaczmarz 125th birthday anniversary, the organizers will also present his biography.

[BB96] H. H. Bauschke and J. Borwein, On projection algorithms for solving convex feasibility problems, SIAM Review 38 (1996), 367-426.
[BBL97] H. H. Bauschke, J. M. Borwein and A. S. Lewis, The method of cyclic projections for closed convex sets in Hilbert space, Contemporary Mathematics 204 (1997), 1-38.
[BC11] H.H. Bauschke and P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, New York, 2011.
[Bre97] C. Brezinski, Projection Methods for Systems of Equations, Studies in Computational Mathematics 7, C. Brezinski and L. Wuytack (eds.) Elsevier, Amsterdam, 1997.
[Byr08] C.L. Byrne, Applied Iterative Methods, AK Peters, Wellesley, MA, 2008.
[Ceg12] A. Cegielski, Iterative Methods for Fixed Point Problems in Hilbert Spaces, Lecture Notes in Mathematics 2057, Springer, Heidelberg, 2012.
[CC15] Y. Censor and A. Cegielski, Projection methods: an annotated bibliography of books and reviews, Optimization, 64 (2015) 2343-2358.
[CZ18] Y.Censor and M. Zaknoon, Algorithms and Convergence Results of Projection Methods for Inconsistent Feasibility Problems: A Review, arXiv:1802.07529v1 (2018).
[CZ98] Y. Censor and S. A. Zenios, Parallel Optimization, Theory, Algorithms and Applications, Oxford University Press, New York, 1997.
[Deu92] F. Deutsch, The method of alternating orthogonal projections, in: Approximation Theory, Spline Functions and Applications, S. P. Singh (ed.), Kluwer Academic Publ., The Netherlands, 1992, pp. 105-121.
[Her09] G.T. Herman, Fundamentals of Computerized Tomography. Image Reconstruction from Projections, Springer, London, 2009.
[Kac37] S. Kaczmarz, Angenäherte Auf‡lösung von Systemen linearer Gleichungen, Bulletin International de l’Académie Polonaise des Sciences et des Lettres A35 (1937), 355-357. English translation: S. Kaczmarz, Approximate solution of systems of linear equations, International Journal of Control 57 (1993), 1269-1271.
[SY98] H. Stark and Y. Yang, Vector Space Projections. A Numerical Approach to Signal and Image Processing, Neural Nets and Optics, Wiley&Sons, New York, 1998.

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