The research activity of Giulia Spaletta principally consists in
studying some Scientific Computation problems, of high complexity
and large dimensions, designing and analysing efficient and
innovative numerical solvers for the problems considered, employing
new generation computing environments.
The research areas of interest can be grouped as follows:
- Numerical Linear Algebra and Parallel Comupting,
- Symbolic Calculus and Approximation, of differential equations
and of experimental data,
even if the theoretical and implementation instruments, employed in
solving the studied problems, relate to both areas.
Within the area of Numerical Linear Algebra and Parallel Computing,
the focus has been on: direct methods for large dimension linear
systems with structure; iterative methods for highly nonlinear
systems; regularization for highly ill conditioned problems;
Medical and Astronomical Imaging; Shape of human glands and their
functional influence.
Within the area of Symbolic Calculus and Approximation, the focus
has been on: ordinary differential equations integrators (ODEs);
Geometric Integration; elementary differential Runge - Kutta
methods (EDRKs); rounding error analysis and automatic
control.
The computational resources used are those of both symbolic and
numerical calculus, available within a particular integrated
Scientific Computations and Computer Algebra environment, that of
Mathematica.
