On generalized bisection of n-simplices
Identifieur interne : 001602 ( PascalFrancis/Curation ); précédent : 001601; suivant : 001603On generalized bisection of n-simplices
Auteurs : R. Horst [Allemagne]Source :
- Mathematics of computation [ 0025-5718 ] ; 1997.
Descripteurs français
- Pascal (Inist)
English descriptors
- KwdEn :
Abstract
A generalized procedure of bisection of n-simplices is introduced, where the bisection point can be an (almost) arbitrary point at one of the longest edges. It is shown that nested sequences of simplices generated by successive generalized bisection converge to a singleton, and an exact bound of the convergence speed in terms of diameter reduction is given. For regular simplices, which mark the worst case, the edge lengths of each worst and best simplex generated by successive bisection are given up to depth n. For n = 2 and 3, the sequence of worst case diameters is provided until it is halved.
pA |
|
---|
Links toward previous steps (curation, corpus...)
- to stream PascalFrancis, to step Corpus: Pour aller vers cette notice dans l'étape Curation :001390
Links to Exploration step
Pascal:97-0302697Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" level="a">On generalized bisection of n-simplices</title>
<author><name sortKey="Horst, R" sort="Horst, R" uniqKey="Horst R" first="R." last="Horst">R. Horst</name>
<affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Department of Mathematics, University of Trier</s1>
<s2>Trier 54286</s2>
<s3>DEU</s3>
<sZ>1 aut.</sZ>
</inist:fA14>
<country>Allemagne</country>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">INIST</idno>
<idno type="inist">97-0302697</idno>
<date when="1997">1997</date>
<idno type="stanalyst">PASCAL 97-0302697 INIST</idno>
<idno type="RBID">Pascal:97-0302697</idno>
<idno type="wicri:Area/PascalFrancis/Corpus">001390</idno>
<idno type="wicri:Area/PascalFrancis/Curation">001602</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">On generalized bisection of n-simplices</title>
<author><name sortKey="Horst, R" sort="Horst, R" uniqKey="Horst R" first="R." last="Horst">R. Horst</name>
<affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Department of Mathematics, University of Trier</s1>
<s2>Trier 54286</s2>
<s3>DEU</s3>
<sZ>1 aut.</sZ>
</inist:fA14>
<country>Allemagne</country>
</affiliation>
</author>
</analytic>
<series><title level="j" type="main">Mathematics of computation</title>
<title level="j" type="abbreviated">Math. comput.</title>
<idno type="ISSN">0025-5718</idno>
<imprint><date when="1997">1997</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><title level="j" type="main">Mathematics of computation</title>
<title level="j" type="abbreviated">Math. comput.</title>
<idno type="ISSN">0025-5718</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Convergence speed</term>
<term>Convex hull</term>
<term>Geometry</term>
<term>Simplex</term>
</keywords>
<keywords scheme="Pascal" xml:lang="fr"><term>Géométrie</term>
<term>Enveloppe convexe</term>
<term>Vitesse convergence</term>
<term>Simplexe</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">A generalized procedure of bisection of n-simplices is introduced, where the bisection point can be an (almost) arbitrary point at one of the longest edges. It is shown that nested sequences of simplices generated by successive generalized bisection converge to a singleton, and an exact bound of the convergence speed in terms of diameter reduction is given. For regular simplices, which mark the worst case, the edge lengths of each worst and best simplex generated by successive bisection are given up to depth n. For n = 2 and 3, the sequence of worst case diameters is provided until it is halved.</div>
</front>
</TEI>
<inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>0025-5718</s0>
</fA01>
<fA02 i1="01"><s0>MCMPAF</s0>
</fA02>
<fA03 i2="1"><s0>Math. comput.</s0>
</fA03>
<fA05><s2>66</s2>
</fA05>
<fA06><s2>218</s2>
</fA06>
<fA08 i1="01" i2="1" l="ENG"><s1>On generalized bisection of n-simplices</s1>
</fA08>
<fA11 i1="01" i2="1"><s1>HORST (R.)</s1>
</fA11>
<fA14 i1="01"><s1>Department of Mathematics, University of Trier</s1>
<s2>Trier 54286</s2>
<s3>DEU</s3>
<sZ>1 aut.</sZ>
</fA14>
<fA20><s1>691-698</s1>
</fA20>
<fA21><s1>1997</s1>
</fA21>
<fA23 i1="01"><s0>ENG</s0>
</fA23>
<fA43 i1="01"><s1>INIST</s1>
<s2>5227</s2>
<s5>354000065245410120</s5>
</fA43>
<fA44><s0>0000</s0>
<s1>© 1997 INIST-CNRS. All rights reserved.</s1>
</fA44>
<fA45><s0>18 ref.</s0>
</fA45>
<fA47 i1="01" i2="1"><s0>97-0302697</s0>
</fA47>
<fA60><s1>P</s1>
</fA60>
<fA61><s0>A</s0>
</fA61>
<fA64 i1="01" i2="1"><s0>Mathematics of computation</s0>
</fA64>
<fA66 i1="01"><s0>USA</s0>
</fA66>
<fC01 i1="01" l="ENG"><s0>A generalized procedure of bisection of n-simplices is introduced, where the bisection point can be an (almost) arbitrary point at one of the longest edges. It is shown that nested sequences of simplices generated by successive generalized bisection converge to a singleton, and an exact bound of the convergence speed in terms of diameter reduction is given. For regular simplices, which mark the worst case, the edge lengths of each worst and best simplex generated by successive bisection are given up to depth n. For n = 2 and 3, the sequence of worst case diameters is provided until it is halved.</s0>
</fC01>
<fC02 i1="01" i2="X"><s0>001A02F01</s0>
</fC02>
<fC02 i1="02" i2="X"><s0>001A02F02</s0>
</fC02>
<fC03 i1="01" i2="1" l="FRE"><s0>Géométrie</s0>
<s3>P</s3>
<s5>01</s5>
</fC03>
<fC03 i1="01" i2="1" l="ENG"><s0>Geometry</s0>
<s3>P</s3>
<s5>01</s5>
</fC03>
<fC03 i1="02" i2="X" l="FRE"><s0>Enveloppe convexe</s0>
<s5>51</s5>
</fC03>
<fC03 i1="02" i2="X" l="ENG"><s0>Convex hull</s0>
<s5>51</s5>
</fC03>
<fC03 i1="02" i2="X" l="SPA"><s0>Cápsula convexa</s0>
<s5>51</s5>
</fC03>
<fC03 i1="03" i2="X" l="FRE"><s0>Vitesse convergence</s0>
<s5>52</s5>
</fC03>
<fC03 i1="03" i2="X" l="ENG"><s0>Convergence speed</s0>
<s5>52</s5>
</fC03>
<fC03 i1="03" i2="X" l="SPA"><s0>Velocidad convergencia</s0>
<s5>52</s5>
</fC03>
<fC03 i1="04" i2="1" l="FRE"><s0>Simplexe</s0>
<s4>CD</s4>
<s5>96</s5>
</fC03>
<fC03 i1="04" i2="1" l="ENG"><s0>Simplex</s0>
<s4>CD</s4>
<s5>96</s5>
</fC03>
<fN21><s1>174</s1>
</fN21>
</pA>
</standard>
</inist>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Rhénanie/explor/UnivTrevesV1/Data/PascalFrancis/Curation
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001602 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/PascalFrancis/Curation/biblio.hfd -nk 001602 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Rhénanie |area= UnivTrevesV1 |flux= PascalFrancis |étape= Curation |type= RBID |clé= Pascal:97-0302697 |texte= On generalized bisection of n-simplices }}
![]() | This area was generated with Dilib version V0.6.31. | ![]() |