# Stable local bases for multivariate spline spaces

Oleg Davydov

Research output: Contribution to journalArticle

12 Citations (Scopus)

### 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 language English 267-297 31 Journal of Approximation Theory 111 2 https://doi.org/10.1006/jath.2001.3577 Published - 2001

### Fingerprint

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

TY - JOUR

T1 - Stable local bases for multivariate spline spaces

AU - Davydov, Oleg

PY - 2001

Y1 - 2001

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

U2 - 10.1006/jath.2001.3577

DO - 10.1006/jath.2001.3577

M3 - Article

VL - 111

SP - 267

EP - 297

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

SN - 0021-9045

IS - 2

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