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Fast Solvers


The course combines a study of the main matrix structures arising in the discretization of integral equations and partial differential equations, an innovative type of analysis of the spectral properties of the resulting large matrices, and advanced numerical methods for the solution of the associated linear systems. More specific items are the following: Discrete Fourier Transform and fast Fourier transform; Generalizations of the FFT to any matrix size; Use of FFT for fast circulant; Toeplitz, polynomial computations; Applications to integral equations coming from restorations of blurred signals (images) with noise; Spectral Analysis of classes of matrices coming from approximations of PDEs (Finite Elements, Finite Differences, Isogeometric Analysis); Classical iterative solvers, Conjugate Gradient, preconditioned CG, Multigrid, and multi-iterative solvers for specific large linear systems coming from the approximation of PDEs; and matrices coming from approximation of Fractional Differential Equations.



Serra Capizzano S.

Course director

Benedusi P.


Additional information

Academic year
Master of Science in Computational Science, Elective course, Lecture, 1st and 2nd year

PhD programme of the Faculty of Informatics, Elective course, Lecture, 1st, 2nd and 3rd year