On the Continuity and Differentiability of a Kind of Fractal Interpolation Function

LI Hong-da; YE Zheng-lin; GAO Hang-shan

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(4): 422-428

LI Hong-da, YE Zheng-lin, GAO Hang-shan. On the Continuity and Differentiability of a Kind of Fractal Interpolation Function[J]. Applied Mathematics and Mechanics, 2002, 23(4): 422-428.

Citation:

LI Hong-da, YE Zheng-lin, GAO Hang-shan. On the Continuity and Differentiability of a Kind of Fractal Interpolation Function[J]. Applied Mathematics and Mechanics, 2002, 23(4): 422-428.

Citation:

LI Hong-da, YE Zheng-lin, GAO Hang-shan. On the Continuity and Differentiability of a Kind of Fractal Interpolation Function[J]. Applied Mathematics and Mechanics, 2002, 23(4): 422-428.

PDF( 301 KB)

On the Continuity and Differentiability of a Kind of Fractal Interpolation Function

1.
State Key Laboratry of Information, Security Graduate School, Chinese Academy of Sciences, Beijing 100039, P. R. China;
2.
Department of Mathematics and Information, Northwestern Polytechnical University, Xi'an 710072, P. R. China;
3.
Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, P. R. China

Received Date: 2000-08-30
Rev Recd Date: 2001-12-21
Publish Date: 2002-04-15

Abstract

Abstract

The sufficient conditions of Helder continuity of two kinds of fractal interpolation functions defined by IFS were obtained. The sufficient and necessary condition for its differentiability was proved. Its derivative was a fractal interpolation function generated by the associated IFS, if it is differentiable.
- fractal,
- interpolation function,
- Helder continuity,
- differentiability

FullText(HTML)

References(10)

References

[1]	Barnsley M F.Fractal functions and interpolation[J].Constr Approx,1986,2(3):303-329.
[2]	Barnsley M F.Fractal Everywhere[M].Boston:Academic Press,1988.
[3]	Massopust Peter R.Fractal function and applications[J].Chaos Solitons & Fractal,1997,8(2):171-190.
[4]	Peter Singer.Self-afine functions and wavelet series[J].J Math Appl,1999,240(2):518-551.
[5]	Jacques Levy-Vehel.Fractal approaches in signal processing[J].Fractals,1995,3(4):715-775.
[6]	Panagiotopoulos P D,Panagouli D.Mechanics on fractal bodies:Data compression using fractal[J].Chaos Solitons & Fractal,1997,8(2):253-267.
[7]	谢和平,孙洪泉.分形插值曲面理论及应用[J].应用数学和力学,1998,19(4):297-306.
[8]	Bedford T.Helder expontents and box dimension for self-affine fractal function[J].Constr Approx,1989,5(1):33-48.
[9]	Donovan G,Geronimo J S,Massopust P R.Construction of orthogonal wavelets using fractal interpolation functions[J].SIAM J Math Anal,1996,27(4):1158-1192.
[10]	Barnsley M F,Harring A N.The calculus of interpolation function[J].J Approx Theory,1989,57(1):14-34.