Cari tutti, a breve ricominceremo con i tradizionali seminari NumPi, questa volta in forma "ibrida".
Per tutti quelli che vorranno ci sarà la possibilità di seguire in presenza in Aula Magna del Dipartimento di Matematica (compilando questa form: https://forms.gle/AaMgajhKhroXdHqY6).
Per gli altri, organizzeremo lo streaming tramite il solito link ( https://hausdorff.dm.unipi.it/b/leo-xik-xu4).
Qui sotto trovate l'annuncio del primo seminario; a breve vi farò avere un Doodle per provare a scegliere un giorno che torni il più comodo possibile a tutti, da utilizzare per quelli successivi.
Trovate tutte le informazioni sulla pagina dei seminari del sito NumPi (https://numpi.dm.unipi.it/seminars).
A presto, -- Leonardo.
Speaker: Igor Simunec Affiliation: Scuola Normale Superiore, Pisa Time: Friday, 15/10/2021, 16:30
Title: Computation of generalized matrix functions with rational Krylov methods
Generalized matrix functions [3] are an extension of the notion of standard matrix functions to rectangular matrices, defined using the singular value decomposition instead of an eigenvalue decomposition. In this talk, we consider the computation of the action of a generalized matrix function on a vector and we present a class of algorithms based on rational Krylov methods [2]. These algorithms incorporate as a special case previous methods based on the Golub-Kahan bidiagonalization [1]. By exploiting the quasiseparable structure of the projected matrices, we show that the basis vectors can be updated using a short recurrence, which can be seen as a generalization to the rational case of the Golub-Kahan bidiagonalization. We also prove error bounds that relate the error of these methods to uniform rational approximation on an interval containing the singular values of the matrix. The effectiveness of the algorithms and the accuracy of the bounds is illustrated with numerical experiments.
This is joint work with Angelo A. Casulli (Scuola Normale Superiore).
[1] F. Arrigo, M. Benzi, and C. Fenu, Computation of generalized matrix functions, SIAM J. Matrix Anal. Appl. 37 (2016), no. 3, 836–860. [2] A. A. Casulli, I. Simunec, Computation of generalized matrix functions with rational Krylov methods, arXiv:2107.12074 (2021). [3] J. B. Hawkins and A. Ben-Israel, On generalized matrix functions, Linear and Multilinear Algebra 1 (1973), no. 2, 163–171.
Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4
Cari tutti, vi ricordo il seminario di oggi alle 16:30 di Igor, in Aula Magna.
-- Leonardo.
On Thu, 2021-10-07 at 14:12 +0200, Leonardo Robol wrote:
Speaker: Igor Simunec Affiliation: Scuola Normale Superiore, Pisa Time: Friday, 15/10/2021, 16:30
Title: Computation of generalized matrix functions with rational Krylov methods
Generalized matrix functions [3] are an extension of the notion of standard matrix functions to rectangular matrices, defined using the singular value decomposition instead of an eigenvalue decomposition. In this talk, we consider the computation of the action of a generalized matrix function on a vector and we present a class of algorithms based on rational Krylov methods [2]. These algorithms incorporate as a special case previous methods based on the Golub-Kahan bidiagonalization [1]. By exploiting the quasiseparable structure of the projected matrices, we show that the basis vectors can be updated using a short recurrence, which can be seen as a generalization to the rational case of the Golub-Kahan bidiagonalization. We also prove error bounds that relate the error of these methods to uniform rational approximation on an interval containing the singular values of the matrix. The effectiveness of the algorithms and the accuracy of the bounds is illustrated with numerical experiments.
This is joint work with Angelo A. Casulli (Scuola Normale Superiore).
[1] F. Arrigo, M. Benzi, and C. Fenu, Computation of generalized matrix functions, SIAM J. Matrix Anal. Appl. 37 (2016), no. 3, 836–860. [2] A. A. Casulli, I. Simunec, Computation of generalized matrix functions with rational Krylov methods, arXiv:2107.12074 (2021). [3] J. B. Hawkins and A. Ben-Israel, On generalized matrix functions, Linear and Multilinear Algebra 1 (1973), no. 2, 163–171.
Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4
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Leonardo Robol