Multiplication
of Short Wavelet Series Using Connection
Coefficients
Valérie Perrier
and Mladen Victor Wickerhauser
Given two functions approximable with short wavelet series, we wish
to find the short wavelet series representing their product. This
can be done by pre-calculating the {\em connection coefficients} which
express the product of two wavelets or scaling functions as a wavelet series.
We follow a method suggested by Daubechies and also used by Dahmen et
al., to rapidly compute these coefficients as elements of a matrix
which solves a fixed-point problem, and derive some of the formulas and
identities satisfied by the coefficients. We estimate the complexity
of the connection coefficient multiplication algorithm by counting
the number of terms, and then illustrate through a series of graphs how
few of these terms are non-negligible.
Advances
in Wavelets,Ka-Sing Lau Ed, ISBN -981-4021-08-3, Springer-Verlag, Singapore,
pp 77--101 (1999)
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