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Archivio digitale delle tesi discusse presso l’Università di Pisa

Tesi etd-04092018-085306


Tipo di tesi
Tesi di laurea magistrale
Autore
ZANOTTO, ROBERTO
URN
etd-04092018-085306
Titolo
Computation of Matrix Functions with Fully Automatic Schur-Parlett and Rational Krylov Methods
Dipartimento
INFORMATICA
Corso di studi
INFORMATICA
Relatori
relatore Prof. Poloni, Federico
controrelatore Prof.ssa Scutellà, Maria Grazia
Parole chiave
  • aaa
  • arnoldi
  • automatic
  • differentiation
  • functions
  • implementation
  • julia
  • krylov
  • matrix
  • parlett
  • rational
  • schur
Data inizio appello
27/04/2018
Consultabilità
Completa
Riassunto
We present MatFun, a Julia package for computing dense and sparse matrix functions fully automatically (no user input required, other than the code to compute the function $f$ and the matrix $A$ themselves). This is achieved by combining specifically chosen algorithms and some peculiar feature of Julia. For dense matrices, the Schur-Parlett algorithm has been implemented, leveraging Julia's automatic differentiation capabilities. The algorithm has also been improved from a performance standpoint, making the Parlett recurrence cache-oblivious and enabling the whole procedure to work mostly in real arithmetic, for real inputs. For sparse matrices, we implemented a Rational Krylov method, alongside the AAA Rational Approximation. Given a function's samples, AAA is often able to accurately identify its poles, which can then be used by the Rational Krylov method itself for the approximation of $f(A)b$. The accuracy and performance of the algorithms are evaluated, in comparison with existing specialized methods.
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