Stability of nonlinear subdivision and multiscale transforms
The authors present a new general sufficient condition for the Lipschitz stability of nonlinear subdivision schemes and multiscale transforms in the univariate case. This extends the results of \textit{A. Cohen, N. Dyn} and \textit{B. Matei} [Appl. Comput. Harmon. Anal. 15, No. 2, 89--116 (2003; Zbl 1046.65071)] for the weighted essentially nonoscillatory scheme and the results of \textit{S. Amat} and \textit{J. Liandrat} [Appl. Comput. Harmon. Anal. 18, No. 2, 198--206 (2005; Zbl 1077.65138)] for the piecewise polynomial harmonic transform. With these techniques it is also possible to prove the stability in some new cases (median interpolating transform, power-p schemes, etc.). The results of this paper are also extendable to other nonlinear multiscale transforms like the normal multiresolution and the manifold-valued subdivision and multiscale transforms.
nonlinear subdivision and multiscale transforms
weighted essentially nonoscillatory scheme
scientific article; zbMATH DE number 5719084
scientific article