Speaker: Giovanni Barbarino
Affiliation: Scuola Normale Superiore, Pisa
Time: Thursday, 15 November 2018, h. 10:00
Place: Sala Seminari Est, Dipartimento di Informatica, Università di
Pisa
Title: Higher order spectral symbols and eigenvalues approximation for
Toeplitz matrices
When modeling natural phenomena with linear partial differential
equations, the discretized system of equations is generally represented
by a sequence of matrices, often coupled with a function called
spectral symbol that enclosures asymptotic spectral information of the
sequence. In fact, when sampling the symbol, we obtain an approximation
of the spectrum of the matrices, with an error having magnitude
inversely proportional with respect to the matrix size. Under
particular hypothesis, the sequence presents an higher-order asymptotic
formula for the eigenvalues, that let us precisely compute the
eigenvalues of large matrices with a technique of
interpolation-extrapolation at a low computational cost and that is
also parallelizable. This algorithm seems also to work on different
kind of matrices, but with irregularities on the extreme eigenvalues,
for which a more accurate analysis is needed.
--
Leonardo Robol