Bertaccini's work in matrix computation devises and analyzes algorithms
for solving numerical multidimensional problems arising in science and
engineering.
He
develops and analyzes fast algorithms for solving large scale systems in
numerical time integration for evolutionary partial
differential
equations
image restoration
advection-diffusion-reaction systems from life sciences
optimization
ordinary differential equations
Applications: Biomedical PDE-based models
(Cochlear models, thermal
ablation of solid tumors), Image restoration models (selective
diffuusion and TV), Numerical optimization
Keywords and phrases: iterative solution of sparse
linear systems; models in biomedical sciences;
implicit methods for evolutionary partial differential equations,
preconditioning for structured and nonstructured linear systems by
incomplete
factorizations; incomplete factorizations and trigonometric
approximations
for preconditioning; preconditioners and iterative methods for shifted
linear
systems; convergence of Krylov-like iterative methods; solution of
ill-conditioned
linear systems.
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