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This article is cited in 9 scientific papers (total in 9 papers)
On a multidimensional analogue of the Schwarz example
V. A. Klyachin
Volgograd State University
Abstract:
We use the Delaunay triangulation to construct a series of examples
showing that in the multidimensional case, in contrast to the
two-dimensional case, the approximation property for derivatives
fails to hold for piecewise-linear approximations of a smooth function.
These examples are closely related to the classical Schwarz example
concerning piecewise-linear approximations of the lateral surface
of a right circular cylinder.
Keywords:
classical Schwarz example, Delaunay triangulation.
DOI:
https://doi.org/10.4213/im6845
 Full text:
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English version:
Izvestiya: Mathematics, 2012, 76:4, 681–687
Bibliographic databases:
     
UDC:
514.174.3
MSC: Primary 65D25; Secondary 53A07, 57R12
Received: 26.01.2011
Citation:
V. A. Klyachin, “On a multidimensional analogue of the Schwarz example”, Izv. RAN. Ser. Mat., 76:4 (2012), 41–48; Izv. Math., 76:4 (2012), 681–687
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http://mi.mathnet.ru/eng/izv6845https://doi.org/10.4213/im6845 http://mi.mathnet.ru/eng/izv/v76/i4/p41
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
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V. A. Klyachin, “Optimizatsiya postroeniya raschetnoi setki dlya resheniya zadachi lokalnogo kriovozdeistviya s ispolzovaniem mnogomernogo geometricheskogo kheshirovaniya na osnove paketa NumPy”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:3 (2014), 355–362
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V. A. Klyachin, D. V. Shurkaeva, “Koeffitsient izoperimetrichnosti simpleksa v zadache approksimatsii proizvodnykh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 15:2 (2015), 151–160
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V. A. Klyachin, E. G. Grigoreva, “Chislennoe issledovanie ustoichivosti ravnovesnykh poverkhnostei s ispolzovaniem paketa NumPy”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 2(27), 17–30
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V. A. Klyachin, “Ekstremalnye svoistva triangulyatsii, osnovannoi na uslovii pustogo vypuklogo mnozhestva”, Sib. elektron. matem. izv., 12 (2015), 991–997
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A. A. Klyachin, A. Yu. Belenikina, “Triangulyatsiya prostranstvennykh elementarnykh oblastei”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2015, no. 4(29), 6–12
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V. A. Klyachin, “Modified Delaunay empty sphere condition in the problem of approximation of the gradient”, Izv. Math., 80:3 (2016), 549–556
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A. V. Boluchevskaya, V. A. Klyachin, M. E. Sapraliev, “Otsenki radiusa prosveta konechnogo mnozhestva edinichnogo shara v ${\mathbb{R}}^{n}$”, Matematicheskaya fizika i kompyuternoe modelirovanie, 20:3 (2017), 6–17
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R. Sh. Khasyanov, “Ermitova interpolyatsiya na simplekse”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:3 (2018), 316–327
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V. A. Klyachin, “Approximation of the gradient of a function on the basis of a special
class of triangulations”, Izv. Math., 82:6 (2018), 1136–1147
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