A Method of the Best Approximation by Fractal Function

Yong-Suk Kang; Myong-Gil Rim

doi:doi:10.11648/j.ijtam.20170301.12

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A Method of the Best Approximation by Fractal Function

Yong-Suk Kang, Myong-Gil Rim

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 1)

Received: 7 September 2016 Accepted: 5 November 2016 Published: 9 December 2016

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Abstract

We present a method constructing a function which is the best approximation for given data and satisfiesthe given self-similar condition. For this, we construct a space F of local self-similar fractal functions and show its properties. Next we present a computational scheme constructing the best fractal approximation in this space and estimate an error of the constructed fractal approximation. Our best fractal approximation is a fixed point of some fractal interpolation function.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 1)
DOI	10.11648/j.ijtam.20170301.12
Page(s)	11-18
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Fractal Interpolation, Fractal Approximation, Iterated Function System, Fractal Function Space

References

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[11]	R. Malysz, The Minkowski dimension of the bivariate fractal interpolation surfaces, Chaos Solitons Fractals 27(5) (2006) 1147–1156.
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Yong-Suk Kang, Myong-Gil Rim. (2016). A Method of the Best Approximation by Fractal Function. International Journal of Theoretical and Applied Mathematics, 3(1), 11-18. https://doi.org/10.11648/j.ijtam.20170301.12

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ACS Style

Yong-Suk Kang; Myong-Gil Rim. A Method of the Best Approximation by Fractal Function. Int. J. Theor. Appl. Math. 2016, 3(1), 11-18. doi: 10.11648/j.ijtam.20170301.12

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AMA Style

Yong-Suk Kang, Myong-Gil Rim. A Method of the Best Approximation by Fractal Function. Int J Theor Appl Math. 2016;3(1):11-18. doi: 10.11648/j.ijtam.20170301.12

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@article{10.11648/j.ijtam.20170301.12,
  author = {Yong-Suk Kang and Myong-Gil Rim},
  title = {A Method of the Best Approximation by Fractal Function},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {1},
  pages = {11-18},
  doi = {10.11648/j.ijtam.20170301.12},
  url = {https://doi.org/10.11648/j.ijtam.20170301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170301.12},
  abstract = {We present a method constructing a function which is the best approximation for given data and satisfiesthe given self-similar condition. For this, we construct a space F of local self-similar fractal functions and show its properties. Next we present a computational scheme constructing the best fractal approximation in this space and estimate an error of the constructed fractal approximation. Our best fractal approximation is a fixed point of some fractal interpolation function.},
 year = {2016}
}

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TY  - JOUR
T1  - A Method of the Best Approximation by Fractal Function
AU  - Yong-Suk Kang
AU  - Myong-Gil Rim
Y1  - 2016/12/09
PY  - 2016
N1  - https://doi.org/10.11648/j.ijtam.20170301.12
DO  - 10.11648/j.ijtam.20170301.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 11
EP  - 18
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170301.12
AB  - We present a method constructing a function which is the best approximation for given data and satisfiesthe given self-similar condition. For this, we construct a space F of local self-similar fractal functions and show its properties. Next we present a computational scheme constructing the best fractal approximation in this space and estimate an error of the constructed fractal approximation. Our best fractal approximation is a fixed point of some fractal interpolation function.
VL  - 3
IS  - 1
ER  -

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Author Information

Yong-Suk Kang

Faculty of Mathematics, Kim Il Sung University, Pyongyang, DPR Korea
Myong-Gil Rim

Faculty of Mathematics, Kim Il Sung University, Pyongyang, DPR Korea

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APA Style

Yong-Suk Kang, Myong-Gil Rim. (2016). A Method of the Best Approximation by Fractal Function. International Journal of Theoretical and Applied Mathematics, 3(1), 11-18. https://doi.org/10.11648/j.ijtam.20170301.12

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ACS Style

Yong-Suk Kang; Myong-Gil Rim. A Method of the Best Approximation by Fractal Function. Int. J. Theor. Appl. Math. 2016, 3(1), 11-18. doi: 10.11648/j.ijtam.20170301.12

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AMA Style

Yong-Suk Kang, Myong-Gil Rim. A Method of the Best Approximation by Fractal Function. Int J Theor Appl Math. 2016;3(1):11-18. doi: 10.11648/j.ijtam.20170301.12

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@article{10.11648/j.ijtam.20170301.12,
  author = {Yong-Suk Kang and Myong-Gil Rim},
  title = {A Method of the Best Approximation by Fractal Function},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {1},
  pages = {11-18},
  doi = {10.11648/j.ijtam.20170301.12},
  url = {https://doi.org/10.11648/j.ijtam.20170301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170301.12},
  abstract = {We present a method constructing a function which is the best approximation for given data and satisfiesthe given self-similar condition. For this, we construct a space F of local self-similar fractal functions and show its properties. Next we present a computational scheme constructing the best fractal approximation in this space and estimate an error of the constructed fractal approximation. Our best fractal approximation is a fixed point of some fractal interpolation function.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - A Method of the Best Approximation by Fractal Function
AU  - Yong-Suk Kang
AU  - Myong-Gil Rim
Y1  - 2016/12/09
PY  - 2016
N1  - https://doi.org/10.11648/j.ijtam.20170301.12
DO  - 10.11648/j.ijtam.20170301.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 11
EP  - 18
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170301.12
AB  - We present a method constructing a function which is the best approximation for given data and satisfiesthe given self-similar condition. For this, we construct a space F of local self-similar fractal functions and show its properties. Next we present a computational scheme constructing the best fractal approximation in this space and estimate an error of the constructed fractal approximation. Our best fractal approximation is a fixed point of some fractal interpolation function.
VL  - 3
IS  - 1
ER  -

Copy | Download