Stable local bases for multivariate spline spaces

Oleg Davydov

Research output: Contribution to journalArticle

12 Citations (Scopus)
4 Downloads (Pure)

Abstract

We present an algorithm for constructing stable local bases for the spaces ${\cal S}_d^r(\triangle)$ of multivariate polynomial splines of smoothness $r\ge1$ and degree $d\ge r2^n+1$ on an arbitrary triangulation $\triangle$ of a bounded polyhedral domain $\Omega\subset\RR^n$, $n\ge2$.
Original languageEnglish
Pages (from-to)267-297
Number of pages31
JournalJournal of Approximation Theory
Volume111
Issue number2
DOIs
Publication statusPublished - 2001

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Multivariate Splines
Triangulation
Splines
Triangle
Polynomials
Polynomial Splines
Multivariate Polynomials
Smoothness
Subset
Arbitrary

Keywords

  • multivariate spline spaces
  • polynomial splines

Cite this

Davydov, Oleg. / Stable local bases for multivariate spline spaces. In: Journal of Approximation Theory . 2001 ; Vol. 111, No. 2. pp. 267-297.
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abstract = "We present an algorithm for constructing stable local bases for the spaces ${\cal S}_d^r(\triangle)$ of multivariate polynomial splines of smoothness $r\ge1$ and degree $d\ge r2^n+1$ on an arbitrary triangulation $\triangle$ of a bounded polyhedral domain $\Omega\subset\RR^n$, $n\ge2$.",
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Stable local bases for multivariate spline spaces. / Davydov, Oleg.

In: Journal of Approximation Theory , Vol. 111, No. 2, 2001, p. 267-297.

Research output: Contribution to journalArticle

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T1 - Stable local bases for multivariate spline spaces

AU - Davydov, Oleg

PY - 2001

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N2 - We present an algorithm for constructing stable local bases for the spaces ${\cal S}_d^r(\triangle)$ of multivariate polynomial splines of smoothness $r\ge1$ and degree $d\ge r2^n+1$ on an arbitrary triangulation $\triangle$ of a bounded polyhedral domain $\Omega\subset\RR^n$, $n\ge2$.

AB - We present an algorithm for constructing stable local bases for the spaces ${\cal S}_d^r(\triangle)$ of multivariate polynomial splines of smoothness $r\ge1$ and degree $d\ge r2^n+1$ on an arbitrary triangulation $\triangle$ of a bounded polyhedral domain $\Omega\subset\RR^n$, $n\ge2$.

KW - multivariate spline spaces

KW - polynomial splines

UR - http://personal.strath.ac.uk/oleg.davydov/kge3.pdf

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DO - 10.1006/jath.2001.3577

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EP - 297

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JF - Journal of Approximation Theory

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