Overview Old Research @ NALAG
An overview of some past research
Old research
Fractional transforms
The fractional Fourier transform is a fractional power of the classical Fourier transform. It is another time-frequency technique that can be used for signal an image analysis.
Rational approximation
The research on rational approximation is related to Padé approximation and hence links up with structrured matrices like Toeplitz and Hankel. More generally the recurrence relations appearing in orthogonal polynomials, rational interpolation etc. are often related to other matrix structures.
Powell-Sabin splines and PDE
Multiresolution ideas in combination with Powell-Sabin splines give rise to subdivision techniques that allow for the design of efficient methods to compute preconditioners for the numerical solution of PDE's by FEM.
Powell-Sabin splines and CAGD
Multiresolution ideas in combination with Powell-Sabin splines give rise to subdivision techniques that allow for local modification of a cagd model.
Wavelets and multiresolution
Also
wavelets
became an important tool in signal and image processing.
This reseach is done in collaboration with
the research group Scientific Computing.
An alternative for the compression of horizon images is given
by normal offsets which is an adaptive
method to catch line disconinuities in images.
Splines and data fitting
Certainly for applications of data fitting the use of spline functions is essential. Spline functions and their use in curve and surface fitting is an important subject with a long tradition in the group. It resulted in a world-wide distributed software package FITPACK.
Didactics research
The members of the group have a heavy
teaching load, mainly in
undergraduate courses. A project was started about
the use of information technology in undergraduate mathematics
courses and the influence that this may have on the
didactics
of undergraduate math teaching.
There are projects visnue and
IPON
for stimulation of active learning in numerical analysis.
Besides the solution of linear systems, also
Subspace methods
iterative methods
for the solution of linear systems or
eigenvalue problems,
such as the
Lanczos
algorithm were done. Research on restarting eigenvalue
solvers has been a main topic.
This research is discontinued since 1998.
ROLLS
A highlight in the integration of linear algebra, linear systems, rational approximation and fast algorithms was certainly the project ROLLS covering Rational Approximation, Orthogonal Functions, Linear Algebra, Linear Systems, and Signal Processing.
Cryptography
With the recent developments in electronic commerce, elliptic curve
cryptosystems
have gained more attention. Because of their relative
short keys, these systems can be implemented in various settings, e.g.
chipcards. The research focusses on the mathematical background, in
cooperation with the department of mathematics.
This research is discontinued since 1999-2000.