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- W2356243071 abstract "A refinement equation of the form φ(x)=∑α∈Z~sa(α)φ(Mx-α),x∈R~s is concerned,where the vector og functions φ=(φ_1,φ_2,…,φ_r)~T∈(L_p(R~s))~r(1≤p≤∞) is unknown,a is a finitely supported sequence of r×r matrices called refinement mask,and M is an s×s integer matrix so that(lim)n→∞M~(-n)=0.The cascade algorithms is associated with a,M generates a sequence φ_n=Q_a~nφ_0,n=1,2,… by Q_aφ(x)=∑α∈Z~sa(α)φ(Mxα),φ∈(L_p(R~s))~r,from a starting vector of function φ_0 in(L_p(R~s))~r(1≤p≤∞).The aim is to give a characterization of convergence rates of the cascade algorithms {φ_n} in terms of the p-norm joint spectral radius of a finite collection of some linear operators determined by a and the set E,where the set E is a complete set of representatives of the distinct cosets of the quotient group Z~s/MZ~s containing 0." @default.
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- W2356243071 date "2006-01-01" @default.
- W2356243071 modified "2023-09-26" @default.
- W2356243071 title "Convergence rates of cascade algorithms in(L_p(R~s))~r(1≤p≤∞)spaces." @default.
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