Title :
A study of refinable function vectors via a nonlinear operator
Author :
Huang, Yhp ; Suter, B.
Author_Institution :
Air Force Inst. of Technol., Wright-Patterson AFB, OH, USA
Abstract :
This paper studies a certain nonlinear operator T from L2 (R,CN) to itself under which every refinable function vector is a fixed point. The iterations Tnf of T on any f∈L2(R,CN) with the Riesz basis property are investigated; they turn out to be the “cascade algorithm” iterates of f with weights depending on f only. The paper also gives conditions for convergence of Tmf to a limit in different topologies
Keywords :
convergence of numerical methods; iterative methods; mathematical operators; signal resolution; vectors; wavelet transforms; Riesz basis property; cascade algorithm; convergence; fixed point; iterations; multiresolution analysis; nonlinear operator; refinable function vectors; topologies; wavelets; Convergence; Equations; Filters; Fourier transforms; Fractals; Interpolation; Military computing; Multiresolution analysis; Topology; Wavelet analysis;
Conference_Titel :
Time-Frequency and Time-Scale Analysis, 1996., Proceedings of the IEEE-SP International Symposium on
Conference_Location :
Paris
Print_ISBN :
0-7803-3512-0
DOI :
10.1109/TFSA.1996.547472