Convexity preserving using GC1 cubic ball interpolation

Samsul Ariffin Abdul Karim, Mohammad Khatim Hasan, Jumat Sulaiman

Research output: Contribution to journalArticle

Abstract

This paper studies the use of cubic Ball interpolation for convexity preserving of scalar data. The parameter ri in the description of the cubic interpolant are subject to be constrained to guarantee the existence of the convex cubic interpolant for convex data. The sufficient condition for the convexity-preserving of cubic Ball interpolant will be developed. The degree smoothness attained is GC1. With suitable choices of the shape parameter, ri the method under consideration is reducing to GC1 quadratic spline shape preserving interpolation for convex data. Several numerical results including with the comparison with existing scheme will be presented to test the applicability of the proposed cubic interpolant.

Original languageEnglish
Pages (from-to)2087-2100
Number of pages14
JournalApplied Mathematical Sciences
Issue number41-44
DOIs
Publication statusPublished - 2014

Fingerprint

Convexity
Interpolants
Interpolation
Ball
Interpolate
Splines
Shape-preserving Interpolation
Quadratic Spline
Spline Interpolation
Shape Parameter
Smoothness
Scalar
Numerical Results
Sufficient Conditions

Keywords

  • Continuity
  • Convexity
  • Cubic ball
  • Interpolation
  • Shape preserving

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Convexity preserving using GC1 cubic ball interpolation. / Karim, Samsul Ariffin Abdul; Hasan, Mohammad Khatim; Sulaiman, Jumat.

In: Applied Mathematical Sciences, No. 41-44, 2014, p. 2087-2100.

Research output: Contribution to journalArticle

Karim, Samsul Ariffin Abdul ; Hasan, Mohammad Khatim ; Sulaiman, Jumat. / Convexity preserving using GC1 cubic ball interpolation. In: Applied Mathematical Sciences. 2014 ; No. 41-44. pp. 2087-2100.
@article{6a5fb3725a3246628a5dc751003b86d3,
title = "Convexity preserving using GC1 cubic ball interpolation",
abstract = "This paper studies the use of cubic Ball interpolation for convexity preserving of scalar data. The parameter ri in the description of the cubic interpolant are subject to be constrained to guarantee the existence of the convex cubic interpolant for convex data. The sufficient condition for the convexity-preserving of cubic Ball interpolant will be developed. The degree smoothness attained is GC1. With suitable choices of the shape parameter, ri the method under consideration is reducing to GC1 quadratic spline shape preserving interpolation for convex data. Several numerical results including with the comparison with existing scheme will be presented to test the applicability of the proposed cubic interpolant.",
keywords = "Continuity, Convexity, Cubic ball, Interpolation, Shape preserving",
author = "Karim, {Samsul Ariffin Abdul} and Hasan, {Mohammad Khatim} and Jumat Sulaiman",
year = "2014",
doi = "10.12988/ams.2014.38481",
language = "English",
pages = "2087--2100",
journal = "Applied Mathematical Sciences",
issn = "1312-885X",
publisher = "Hikari Ltd.",
number = "41-44",

}

TY - JOUR

T1 - Convexity preserving using GC1 cubic ball interpolation

AU - Karim, Samsul Ariffin Abdul

AU - Hasan, Mohammad Khatim

AU - Sulaiman, Jumat

PY - 2014

Y1 - 2014

N2 - This paper studies the use of cubic Ball interpolation for convexity preserving of scalar data. The parameter ri in the description of the cubic interpolant are subject to be constrained to guarantee the existence of the convex cubic interpolant for convex data. The sufficient condition for the convexity-preserving of cubic Ball interpolant will be developed. The degree smoothness attained is GC1. With suitable choices of the shape parameter, ri the method under consideration is reducing to GC1 quadratic spline shape preserving interpolation for convex data. Several numerical results including with the comparison with existing scheme will be presented to test the applicability of the proposed cubic interpolant.

AB - This paper studies the use of cubic Ball interpolation for convexity preserving of scalar data. The parameter ri in the description of the cubic interpolant are subject to be constrained to guarantee the existence of the convex cubic interpolant for convex data. The sufficient condition for the convexity-preserving of cubic Ball interpolant will be developed. The degree smoothness attained is GC1. With suitable choices of the shape parameter, ri the method under consideration is reducing to GC1 quadratic spline shape preserving interpolation for convex data. Several numerical results including with the comparison with existing scheme will be presented to test the applicability of the proposed cubic interpolant.

KW - Continuity

KW - Convexity

KW - Cubic ball

KW - Interpolation

KW - Shape preserving

UR - http://www.scopus.com/inward/record.url?scp=84899528051&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899528051&partnerID=8YFLogxK

U2 - 10.12988/ams.2014.38481

DO - 10.12988/ams.2014.38481

M3 - Article

SP - 2087

EP - 2100

JO - Applied Mathematical Sciences

JF - Applied Mathematical Sciences

SN - 1312-885X

IS - 41-44

ER -