Advances in Computational Mathematics

, Volume 30, Issue 2, pp 177–200

Spline wavelets on the interval with homogeneous boundary conditions

Article

DOI: 10.1007/s10444-008-9064-9

Cite this article as:
Jia, RQ. Adv Comput Math (2009) 30: 177. doi:10.1007/s10444-008-9064-9

Abstract

In this paper we investigate spline wavelets on the interval with homogeneous boundary conditions. Starting with a pair of families of B-splines on the unit interval, we give a general method to explicitly construct wavelets satisfying the desired homogeneous boundary conditions. On the basis of a new development of multiresolution analysis, we show that these wavelets form Riesz bases of certain Sobolev spaces. The wavelet bases investigated in this paper are suitable for numerical solutions of ordinary and partial differential equations.

Keywords

Spline waveletsWavelets on the intervalSlant matricesMultiresolution analysisRiesz basesSobolev spaces

Mathematics Subject Classifications (2000)

42C4041A1546B15

Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada