Abstract
Recently algebraic polynomials have been considered as wavelets and handled
by wavelet techniques. In the unified approach for the construction of
polynomial wavelets by Fischer and Prestin, the actual implementation of
decomposition, reconstruction and/or compression schemes required at each
level the inversion of generalized Grammian matrices, in general not
orthogonal. In this context the present paper works out necessary and
sufficient conditions for the polynomial wavelets to be orthogonal to each
other. Furthermore it shows how these computable characterizations lead to
attractive decomposition and reconstruction algorithms based on orthogonal
matrices. Finally the special case of Bernstein--Szego weight functions is
studied in detail.
Anno
2002
Autori IAC
Tipo pubblicazione
Altri Autori
Fischer B., Themistoclakis W.
Editore
Baltzer Science Publishers
Rivista
Numerical algorithms