### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | Universiteit Twente |

Number of pages | 4 |

Publication status | Published - 1998 |

### Publication series

Name | Memorandum Faculteit TW |
---|---|

Publisher | Universiteit Twente |

No. | 1457 |

### Keywords

- MSC-41A29
- METIS-141108
- IR-30468
- Convexity preservation
- MSC-65D17
- EWI-3277
- Stationary subdivision scheme
- MSC-65D05
- MSC-41A05

### Cite this

*Convexity preservation of the four-point interpolatory subdivision scheme*. (Memorandum Faculteit TW; No. 1457). Enschede: Universiteit Twente.

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*Convexity preservation of the four-point interpolatory subdivision scheme*. Memorandum Faculteit TW, no. 1457, Universiteit Twente, Enschede.

**Convexity preservation of the four-point interpolatory subdivision scheme.** / Dyn, Nira; Kuijt, F.; Levin, David; van Damme, Rudolf M.J.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Convexity preservation of the four-point interpolatory subdivision scheme

AU - Dyn, Nira

AU - Kuijt, F.

AU - Levin, David

AU - van Damme, Rudolf M.J.

N1 - Imported from MEMORANDA

PY - 1998

Y1 - 1998

N2 - In this note we examine the convexity preserving properties of the (linear) four-point interpolatory subdivision scheme of Dyn, Gregory and Levin when applied to functional univariate strictly-convex data. Conditions on the tension parameter guaranteeing preservation of convexity are derived. These conditions depend on the initial data. The resulting scheme is the four-point scheme with tension parameter bounded from above by a bound smaller than $1/16$. Thus the scheme generates $C^1$ limit functions and has approximation order two.

AB - In this note we examine the convexity preserving properties of the (linear) four-point interpolatory subdivision scheme of Dyn, Gregory and Levin when applied to functional univariate strictly-convex data. Conditions on the tension parameter guaranteeing preservation of convexity are derived. These conditions depend on the initial data. The resulting scheme is the four-point scheme with tension parameter bounded from above by a bound smaller than $1/16$. Thus the scheme generates $C^1$ limit functions and has approximation order two.

KW - MSC-41A29

KW - METIS-141108

KW - IR-30468

KW - Convexity preservation

KW - MSC-65D17

KW - EWI-3277

KW - Stationary subdivision scheme

KW - MSC-65D05

KW - MSC-41A05

M3 - Report

T3 - Memorandum Faculteit TW

BT - Convexity preservation of the four-point interpolatory subdivision scheme

PB - Universiteit Twente

CY - Enschede

ER -