Software produced by members of the MaSeteam
Algorithms for the Geronimus transformation for orthogonal polynomials on the unit circle
Here
the interested reader can download the software used to produce the
experimental results in the report and corresponding paper:
 M. Humet, and M. Van Barel,
Algorithms for the Geronimus transformation for orthogonal polynomials on the unit circle,
Department of Computer Science,
K.U.Leuven, Report TW ???, Leuven, Belgium, January, 2012
 M. Humet, and M. Van Barel,
Algorithms for the Geronimus transformation for orthogonal polynomials on the unit circle,
Submitted, January, 2012
The archive contains the Matlab files of the algorithms that appear in the paper.
Moreover we provide the script to reproduce all the plots of the paper.
The following files are included:
Script to generate all the plots of the report. NOTE that a lot of high precision calculations are done using the VPA function in the Symbolic Math Toolbox of Matlab, so running it takes a few minutes:
algorithms of the paper:
 christoffel.m
 geronimus_bwd.m
 geronimus_fwd_st.m
 geronimus_fwd_direct.m
set of tools used in algorithms and scripts, documentation appears in the files themselves:
 givens_alg.m
 givensfactors.m
 givprod.m
 moments_posdef.m
 r2c.m
 reflection.m
 ST.m
 uvarov_moments.m
 valid_m_range.m
help function to plot:
A Superfast Solver for Real Symmetric Toeplitz Systems Using Real
Trigonometric Transformations
Here
the interested reader can download the software used to produce the
experimental results in the report:
 G. Codevico, G. Heinig, and M. Van Barel, A
superfast solver for real symmetric Toeplitz systems using real
trigonometric transformations, Department of Computer Science,
K.U.Leuven, Report TW 386, Leuven, Belgium, February, 2004
Semiseparable matrices and the symmetric eigenvalue
problem
We refer the interested reader to the
software corresponding to the PhDthesis of Raf Vandebril.
An implicit QRalgorithm to compute the eigensystem
of symmetric semiseparable matrices
The Matlabfiles as a tarredfile.
Reference:
Solving diagonalplussemiseparable systems using a
QR or a URV decomposition
The Matlabfiles as a zippedfile.
Reference:
Reducing a symmetric matrix by orthogonal similarity
transformations into a semiseparable matrix
and the link with the LanczosRitz values
The Matlabfiles as a zippedfile or as a tarredfile.
Reference
A fast (block) Hankel solver
Click here to download our fast Hankel
solver.
The corresponding package for block Hankel matrices can be found here.
Both packages are written in Fortran 90.
They were compiled and tested using the xlf90 compiler on an IBM
RS6000.
Matlab mfiles are available via anonymous ftp to ftp.mathworks.com.
Look for the files hsolve.m,
ratint.m,
block_hsolve.m
and block_ratint.m
in the directory /pub/contrib/v4/linalg.
References:

P. Kravanja and M. Van Barel, A fast Hankel solver based on an
inversion
formula for Loewner matrices. Linear Algebr. Appl. 282(13):275295,
1998.

P. Kravanja and M. Van Barel, A fast block Hankel solver based on
an
inversion formula for block Loewner matrices, CALCOLO 33(12):147164,
JanuaryJune 1996. Proceedings of the workshop Toeplitz Matrices:
Structure,
Algorithms and Applications, Cortona (Italy), September 912, 1996.
A superfast Toeplitz solver
Click here to download our
superfast
Toeplitz solver.
This package is written in Fortran 90.
It was compiled and tested using the xlf90 compiler on an IBM RS6000
and the f90 compiler on a Sun SPARC.
Reference:

M. Van Barel, G. Heinig and P. Kravanja A stabilized superfast
solver
for indefinite Toeplitz systems (In preparation)
Solving a multivariate polynomial interpolation problem
Click here to download the
implementation
in Maple.
Reference:

R. Vandebril, M. Van Barel, O. Ruatta, B. Mourrain A new algorithm
for
multivariate polynomial interpolation problems (In preparation)