Numerics and fractals (Q2928535)

The authors are dealing with so called local iterated function systems (IFS). Let \(X\) be a complete metric space. A local IFS in \(X\) is a finite family of pairs \((X_{i}, f_{i})\), where \(X_i\) are subsets of \(X\), and \(f_i\) are continuous mappings \(f_{i}: X_{i}\mapsto X\). The authors discuss the numerical applications of local IFSs which are not based on a basis of a linear space but on the IFS itself. They define local fractal functions and show that these functions are the fixed points of a Read--Bajactarevic operator, which can be described in terms of matrices acting on vectors of function values over grids. The paper is concluded with some general remarks concerning, in particular, a connection between fractals and the active research area of tensor approximation.