#### Abstract

The majority of the research done into creating balanced multiwavelets has involved establishing a series of conditions on the mask of the new scaling vector by solving a large nonlinear system. The result is a completely different new function vector solution to the dilation equation with the new matrix coefficients. The research presented here will show a way to use previously-constructed orthonormal scaling vectors to generate equivalent orthonormal scaling vectors that are balanced up to the approximation order of the previous scaling vector. The technique uses linear combinations of the integer translates of the previous-constructed scaling vector.

#### Disciplines

Applied Mathematics | Mathematics

#### Recommended Repository Citation

Kessler, Bruce. (2005). Balanced Scaling Vectors Using Linear Combinations of Existing Scaling Vectors. *Approximation Theory XI: Gatlinburg*, 197-208.

**Available at:**
https://digitalcommons.wku.edu/math_fac_pub/3

## Comments

Originally published in

Approximation Theory XI: Gatlinburg 2004, edited by C.K. Chui, M. Neamtu, and L.L. Schumaker, Nashboro Press, Brentwood, TN (2005): 197-208. ISBN 0-9728482-5-8.