Georgia Institute of Technology College of Sciences

The Alpert multiwavelets are an extension of the Haar wavelet to higher degree piecewise polynomials thereby giving higher approximation order. This system has uses in numerical analysis in problems where shocks develop. An orthogonal basis of scaling functions for this system are the Legendre polynomials and we will examine the consequence of this. In particular we will show that the coefficients in the refinement equation can be written in terms of Jacobi polynomials with varying parameters. Difference equationssatisfied by these coefficients will be exhibited that give rise to generalized eigenvalue problems. Furthermore an orthogonal basis of wavelet functions will be discussed that have explicit formulas as hypergeometric polynomials.