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Fractal Interpolation Functions (FIF) and hidden variable FIF are used to approximate self-affine and non-self-affine objects respectively. To approximate, both type of data from a single IFS, the construction of Coalescence FIF is introduced. Their smoothness analysis is carried out through operator approximation. Results concerning on fractal dimension, stability and integral moment theory of Coalescence Affine FIFs are studied. Coalescence Bivariate Fractal Interpolation Surfaces (CBFIS) are developed in the present work by defining suitable vector-valued IFS. The effects of hidden variables on CBFIS and its roughness factors are also studied. The generalized spline FIF with any type of boundary conditions is introduced. The existence and methods of construction through moments and the convergence results of Cubic Spline FIFs are initiated in the present work. Coalescence Spline FIFs are introduced; their existence and method of construction are derived. Finally, Coalescence Cubic Spline FIFs are also constructed here through moments and their convergence results towards the original function are obtained.
About the author
A.K.B.Chand is Assistant Professor of Mathematics at IIT Madras, Chennai, India. After completing his doctorate at IIT Kanpur, he worked as a faculty member at BITS Pilani- Goa Campus, Vasco and as a Post-doctoral fellow at the University of Zaragoza, Spain. His research interest includes Fractals, Approximation Theory, Wavelets and CAGD.
