Geodesic
Portrait of the roots of a system of equations
Matematičeskoe obrazovanie, no. 3 (2022), pp. 33-46 
V. F. Ochkov; Yu. V. Chudova; N. R. Umirova. Portrait of the roots of a system of equations. Matematičeskoe obrazovanie, no. 3 (2022), pp. 33-46. http://geodesic.mathdoc.fr/item/MO_2022_3_a3/
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     author = {V. F. Ochkov and Yu. V. Chudova and N. R. Umirova},
     title = {Portrait of the roots of a system of equations},
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     pages = {33--46},
     year = {2022},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2022_3_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The article describes a new unusual approach to assessing the quality of numerical optimization methods and solving systems of equations, based on the analysis of areas of attraction of singular points - extrema and roots. Along the way, objects of modern fine art (design) with mathematical and even mystical meanings are generated. A specific system of equations is considered as a person from whom a portrait is being painted. The applied methods of numerical solution of the system of equations are the individual styles of a particular artist.

[1] V. F. Ochkov, “Reshenie algebraicheskikh uravnenii i sistem ili Van Gog v srede Mathcad”, KompyuterPress., 2001, no. 9 http://www.twt.mpei.ac.ru/ochkov/Carpet/index.htm

[2] V. F. Ochkov, A. V. Bobryakov, S. N. Khorkov, “Gibridnoe reshenie zadach na kompyutere”, Cloud of Science, 4:2 (2017), 5–26 http://twt.mpei.ac.ru/ochkov/Hybrid.pdf

[3] Maarten van Turnhout, Florian Bociort, “Chaotic behavior in an algorithm to escape from poor local minima in lens design”, Opt. Express, 17 (2009), 6436–6450 https://opg.optica.org/oe/fulltext.cfm?uri=oe-17-8-6436