Volume 3, Issue 3
Coalescence Cubic Spline Fractal Interpolation Surfaces.

ARYA KUMAR BEDABRATA CHAND

Int. J. Numer. Anal. Mod. B,3 (2012), pp. 207-223

Published online: 2012-03

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  • Abstract
Fractal geometry provides a new insight to the approximation and modelling of scientific data.This paper presents the construction of coalescence cubic spline fractal interpolation surfaces over a rectangular grid D through the corresponding univariate basis of coalescence cubic fractal splines of Type-I or Type-II. Coalescence cubic spline fractal surfaces are self-affine or nonself- affine in nature depending on the iterated function systems parameters of these univariate fractal splines. Upper bounds of L_∞-norm of the errors between between a coalescence cubic spline fractal surface and an original function f ∈ C^4[D], and their derivatives are deduced. Finally, the effects of free variables, constrained free variables and hidden variables are discussed for coalescence cubic spline fractal interpolation surfaces through suitably chosen examples.
  • AMS Subject Headings

28A80 41A05 41A15 41A25 65D10 65D17

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COPYRIGHT: © Global Science Press

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@Article{IJNAMB-3-207, author = {ARYA KUMAR BEDABRATA CHAND}, title = {Coalescence Cubic Spline Fractal Interpolation Surfaces.}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2012}, volume = {3}, number = {3}, pages = {207--223}, abstract = {Fractal geometry provides a new insight to the approximation and modelling of scientific data.This paper presents the construction of coalescence cubic spline fractal interpolation surfaces over a rectangular grid D through the corresponding univariate basis of coalescence cubic fractal splines of Type-I or Type-II. Coalescence cubic spline fractal surfaces are self-affine or nonself- affine in nature depending on the iterated function systems parameters of these univariate fractal splines. Upper bounds of L_∞-norm of the errors between between a coalescence cubic spline fractal surface and an original function f ∈ C^4[D], and their derivatives are deduced. Finally, the effects of free variables, constrained free variables and hidden variables are discussed for coalescence cubic spline fractal interpolation surfaces through suitably chosen examples.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/279.html} }
TY - JOUR T1 - Coalescence Cubic Spline Fractal Interpolation Surfaces. AU - ARYA KUMAR BEDABRATA CHAND JO - International Journal of Numerical Analysis Modeling Series B VL - 3 SP - 207 EP - 223 PY - 2012 DA - 2012/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/279.html KW - Fractals KW - Iterated Function System KW - Fractal Interpolation Surface KW - Cardinal Cubic Spline KW - Hidden Variables KW - CHFIS KW - Non-self-affine and Surface Approximation AB - Fractal geometry provides a new insight to the approximation and modelling of scientific data.This paper presents the construction of coalescence cubic spline fractal interpolation surfaces over a rectangular grid D through the corresponding univariate basis of coalescence cubic fractal splines of Type-I or Type-II. Coalescence cubic spline fractal surfaces are self-affine or nonself- affine in nature depending on the iterated function systems parameters of these univariate fractal splines. Upper bounds of L_∞-norm of the errors between between a coalescence cubic spline fractal surface and an original function f ∈ C^4[D], and their derivatives are deduced. Finally, the effects of free variables, constrained free variables and hidden variables are discussed for coalescence cubic spline fractal interpolation surfaces through suitably chosen examples.
ARYA KUMAR BEDABRATA CHAND. (2012). Coalescence Cubic Spline Fractal Interpolation Surfaces.. International Journal of Numerical Analysis Modeling Series B. 3 (3). 207-223. doi:
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