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Izvestiya: Mathematics, 2012, Volume 76, Issue 4, Pages 681–687
DOI: https://doi.org/10.1070/IM2012v076n04ABEH002601 (Mi im6845) 		 
This article is cited in 12 scientific papers (total in 12 papers)

On a multidimensional analogue of the Schwarz example

V. A. Klyachin

Volgograd State University
English version PDF (198 kB) Citations (12)
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DOI: https://doi.org/10.1070/IM2012v076n04ABEH002601
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.
Received: 26.01.2011
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2012, Volume 76, Issue 4, Pages 41–48
DOI: https://doi.org/10.4213/im6845
Bibliographic databases:
Document Type: Article
UDC: 514.174.3
MSC: Primary 65D25; Secondary 53A07, 57R12
Language: English
Original paper language: Russian
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://www.mathnet.ru/eng/im/v76/i4/p41
    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:662
    Russian version PDF:238
    English version PDF:5
    References:69
    First page:35
     
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