Lattices on simplicial partitions

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Title:	Lattices on simplicial partitions
Authors:	ID Jaklič, Gašper (Author) ID Kozak, Jernej (Author) ID Knez, Marjetka (Author) ID Vitrih, Vito (Author) ID Žagar, Emil (Author)
Files:	http://dx.doi.org/10.1016/j.cam.2009.02.022
Language:	English
Work type:	Not categorized
Typology:	1.08 - Published Scientific Conference Contribution
Organization:	IAM - Andrej Marušič Institute
Abstract:	In this paper, a $(d+1)$ -pencil lattices on a simplex in ${\mathbb{R}}^d$ are studied. The barycentric approach naturally extends the lattice from a simplex to a simplicial partition, providing a continuous piecewise polynomial interpolant over the extended lattice. The number of degrees of freedom is equal to the number of vertices of the simplicial partition. The constructive proof of thisfact leads to an efficient computer algorithm for the design of a lattice.
Keywords:	numerical analysis, lattice, barycentric coordinates, simplicial partition
Year of publishing:	2010
Number of pages:	Str. 1704-1715
PID:	20.500.12556/RUP-7729
ISSN:	0377-0427
UDC:	519.65
DOI:	10.1016/j.cam.2009.02.022
COBISS.SI-ID:	15087705
Publication date in RUP:	03.04.2017
Views:	2699
Downloads:	138
Metadata:
:	JAKLIČ, Gašper, KOZAK, Jernej, KNEZ, Marjetka, VITRIH, Vito and ŽAGAR, Emil, 2010, Lattices on simplicial partitions. In : [online]. Published Scientific Conference Contribution. 2010. p. 1704–1715. [Accessed 5 April 2025]. Retrieved from: http://dx.doi.org/10.1016/j.cam.2009.02.022 Copy citation

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Language:	Slovenian
Title:	Mreže na simplicialnih particijah
Abstract:	V članku so obravnavane mreže na simplicialnih particijah v ${\mathbb{R}}^d$ . Z naravno posplošitvijo baricentričnega pristopa mrežo razširimo s simpleksa na simpleksno particijo, in dobimo zvezen odsekoma polinomski interpolant nad razširjeno mrežo. Število prostostnih stopenj je enako številu točk simplicialne particije. Konstruktivni dokaz vodi do učinkovitega algoritma za konstrukcijo mreže.
Keywords:	numerična analiza, mreža, baricentrične koordinate, simplicialna particija

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