**Maple Routines for Constructing Pairs of Dual Wavelet Frames**- Format of program: Maple 7.0 routines
- Files for downloading:
- Related papers:
- The program is mainly based on the algorithms described in the following paper:
- Ingrid Daubechies and Bin Han, Pairs of dual wavelet frames from any two refinable functiosn, Constructive Approximation, Vol. 20 (2004), No. 3, 325--352. [Abstract].

**Computing Smoothness of Refinable Functions Uisng Symmetry**- Format of program:
- C programs calling MATLAB routine eig for computing eigenvalues.

- Files for downloading:
- copyright Notice and copyright.
- README Read me file.
- makefile
- d1sm.c To compute the Sobolev smoothness and the Hoelder smoothness (when the symbol of the mask is nonnegative) of symmetric refinable functions in 1D with a dilation factor by taking the advantages of the symmetry of the refinable functions. It can also handle masks without symmetry.
- d2sm.c To compute the Sobolev smoothness and the Hoelder smoothness (when the symbol of the mask is nonnegative) of symmetric refinable functions in 2D with a dilation matrix by taking the advantages of the symmetry of the refinable functions. It can also handle masks without symmetry.
- oldsm.c. Computing Sobolev smoothness for 1D/2D/3D symmetric refinable functions with dilation matrix 2I.
- butterfly. An example of the format of the input 2D mask for Butterfly.

- Related papers:
- The programs are based on the algorithms described in the paper:
- Bin Han, Computing the smoothness exponent of a symmetric multivariate refinable function, SIAM Journal on Matrix Analysis and its Applications, Vol. 24 (2003), No. 3, 693--714. [Abstract], [PDF].
- For detail about symmetry group of a mask, see, Bin Han, Symmetry property and construction of wavelets with a general dilation matrix, Linear Algebra and its Applications, Vol. 353 (2002), 207--225.
- Also see other references cited in the above papers, or for some related papers click here.

- Other pointers:
- Matlab routines by Peter Oswald
- Matlab rountines by Qing-Tang Jiang
- Matlab routines with interface the IGPM Villemoes Machine by the group at RWTH, Germany
- Comments: Symmetry of the refinable functions is not taken into account in computation in the above programs. If you know other pointers on computing smoothness of a refinable function, please email me.

**CBC Algorithms for Constructing Multivariate Biorthogonal Multiwavelets**- Format of program: Maple 6.0 routines
- Files for downloading:
- copyright Notice and copyright.
- README Read me file.
- basicall. Some basic maple routines for converting between different formats.
- d1cbc CBC algorithms and other useful routines in constructing 1-dimensional multiwavelets with any given multiplicity and any given dilation factor.
- d2cbc CBC algorithms and other useful routines in constructing 2-dimensional multiwavelets with any given multiplicity and any given dilation 2 by 2 dilation matrix.
- example1. Some examples for using the programs to construct 1-dimensional Hermite interpolatory mask and its dual masks by CBC algorithm.
- example2. Some examples for using the programs to construct 2-dimensional Hermite interpolatory mask and its dual masks by CBC algorithm with the quincunx dilation matrix.

- Related papers:
- The programs are mainly based on the algorithms described in the following paper:
- Bin Han, Approximation Properties and Construction of Hermite Interpolants and Biorthogonal Multiwavelets, Journal of Approximation Theory, Vol. 110 (2001), No.1, 18--53. [Abstract],
- For more details about the CBC algorithm, check other papers on CBC algorithm here.

- Other pointers:
- Comments: If you know other pointers of softwares on constructing multivariate wavelets, please email me.

This page was revised by Bin Han on April 16, 2004. bhan@ualberta.ca