1. Fractal interpolation on the real projective plane.
- Author
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Hossain, Alamgir, Akhtar, Md. Nasim, and Navascués, Maria A.
- Subjects
- *
PROJECTIVE geometry , *INTERPOLATION , *MATHEMATICAL analysis , *PROJECTIVE planes , *PROJECTIVE spaces , *NUMERICAL analysis - Abstract
Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections, and mappings. Projective geometry identifies a line with a single point, like the perspective on the horizon line and, due to this fact, it requires a restructuring of the real mathematical and numerical analysis. In particular, the problem of interpolating data must be refocused. In this paper, we define a linear structure along with a metric on a projective space, and prove that the space thus constructed is complete. Then, we consider an iterated function system giving rise to a fractal interpolation function of a set of data. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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