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Izv. RAN. Ser. Mat., 2012, Volume 76, Issue 4, Pages 41–48 (Mi izv6845)  

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: PDF file (412 kB)
References: PDF file   HTML file

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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  • https://doi.org/10.4213/im6845
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    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:
    1. 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  mathnet  crossref  elib
    2. 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  mathnet  crossref  elib
    3. 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  mathnet  crossref
    4. V. A. Klyachin, “Ekstremalnye svoistva triangulyatsii, osnovannoi na uslovii pustogo vypuklogo mnozhestva”, Sib. elektron. matem. izv., 12 (2015), 991–997  mathnet  crossref
    5. 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  mathnet  crossref
    6. V. A. Klyachin, “Modified Delaunay empty sphere condition in the problem of approximation of the gradient”, Izv. Math., 80:3 (2016), 549–556  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. 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  mathnet  crossref
    8. R. Sh. Khasyanov, “Ermitova interpolyatsiya na simplekse”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:3 (2018), 316–327  mathnet  crossref  elib
    9. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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