Biorthogonal Spline Wavelets on the Interval

We investigate biorthogonal spline wavelets on the interval. We give sufficient and necessary conditions for the reconstruction and decomposition matrices to be sparse. Furthermore, we give numerical estimates for the Riesz stability of such bases. §

[1]  E. Quak,et al.  Decomposition and Reconstruction Algorithms for Spline Wavelets on a Bounded Interval , 1994 .

[2]  C. Chui,et al.  Wavelets on a Bounded Interval , 1992 .

[3]  C. D. Boor,et al.  Spline approximation by quasiinterpolants , 1973 .

[4]  I. Daubechies,et al.  Biorthogonal bases of compactly supported wavelets , 1992 .

[5]  E. Quak,et al.  Multivariate Approximation and Applications: Theory and algorithms for nonuniform spline wavelets , 2001 .

[6]  Charles A. Micchelli,et al.  Banded matrices with banded inverses , 1992 .

[7]  K. Mørken.  On Total Positivity of the Discrete Spline Collocation Matrix , 1996 .

[8]  Karsten Urban,et al.  Adaptive wavelet methods using semiorthogonal spline wavelets: Sparse evaluation of nonlinear functions , 2003 .

[9]  Kai Bittner,et al.  A new view on biorthogonal spline wavelets , 2005 .

[10]  Tor Berger,et al.  Exact Reconstruction Algorithms for the Discrete Wavelet Transform Using Spline Wavelets , 1995 .

[11]  Wolfgang Dahmen,et al.  Nonlinear functionals of wavelet expansions – adaptive reconstruction and fast evaluation , 2000, Numerische Mathematik.

[12]  T. Lyche,et al.  Making the Oslo algorithm more efficient , 1986 .

[13]  W. Dahmen,et al.  Biorthogonal Spline Wavelets on the Interval—Stability and Moment Conditions , 1999 .

[14]  Tom Lyche,et al.  Theory and Algorithms for Non-Uniform Spline Wavelets , 2001 .

[15]  Tom Lyche,et al.  Discrete B-splines and subdivision techniques in computer-aided geometric design and computer graphics , 1980 .

[16]  C. R. Deboor,et al.  A practical guide to splines , 1978 .

[17]  Kai Bittner,et al.  Fast Algorithms for Periodic Spline Wavelets on Sparse Grids , 1999, SIAM J. Sci. Comput..

[18]  L. Schumaker.  Spline Functions: Basic Theory , 1981 .

[19]  Rob Stevenson,et al.  Locally Supported, Piecewise Polynomial Biorthogonal Wavelets on Nonuniform Meshes , 2000 .