Counterexamples in parameter identification problem of the fractal interpolation functions. (English) Zbl 1024.41001
Summary: Fractal interpolation functions provide a new method to model experimental data. L. Dalla and V. Drakopoulos got some conditions that a vertical scaling factor must obey to model effectively an arbitrary function [J. Approximation Theory 101, 289-302 (1999; Zbl 0945.41001)]. In this paper, we present certain counterexamples to show that the converse does not hold.
MSC:
| 41A05 | Interpolation in approximation theory |
| 41A30 | Approximation by other special function classes |
| 28A80 | Fractals |
Citations:
Zbl 0945.41001References:
| [1] | Barnsley, M. F., Fractal functions and interpolation, Constr. Approx., 2, 303-329 (1986) · Zbl 0606.41005 |
| [2] | Dalla, L.; Drakopoulos, V., On the parameter identification problem in the plane and the polar fractal interpolation functions, J. Approx. Theory, 101, 289-302 (1999), doi:10.1006/jath.1999.3380 · Zbl 0945.41001 |
| [3] | Ruan, H.-J.; Sha, Z., Solving inverse problems of FIF by interpolating operator, Chinese J. Numer. Math. Appl., 22, 3, 1-11 (2000) · Zbl 0987.41008 |
| [4] | H.-J. Ruan, Z. Sha, W.-Y. Su, Parameter identification problem of the fractal interpolation functions, Numer. Math. J. Chinese Univ. (English series) (2003), to appear.; H.-J. Ruan, Z. Sha, W.-Y. Su, Parameter identification problem of the fractal interpolation functions, Numer. Math. J. Chinese Univ. (English series) (2003), to appear. · Zbl 1059.28010 |
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