We consider the numerical approximation of f(A) b where b∈ RN and A is the sum of Kronecker products, that is A= M2⊗ I+ I⊗ M1∈ RN×N. Here f is a regular function such that f(A) is well defined. We derive a computational strategy that significantly lowers the memory requirements and computational efforts of the standard approximations, with special emphasis on the exponential and on completely monotonic functions, for which the new procedure becomes particularly advantageous. Our findings are illustrated by numerical experiments with typical functions used in applications.

Approximation of functions of large matrices with Kronecker structure

SIMONCINI, VALERIA
2017

Abstract

We consider the numerical approximation of f(A) b where b∈ RN and A is the sum of Kronecker products, that is A= M2⊗ I+ I⊗ M1∈ RN×N. Here f is a regular function such that f(A) is well defined. We derive a computational strategy that significantly lowers the memory requirements and computational efforts of the standard approximations, with special emphasis on the exponential and on completely monotonic functions, for which the new procedure becomes particularly advantageous. Our findings are illustrated by numerical experiments with typical functions used in applications.
2017
Benzi, Michele; Simoncini, Valeria
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/586014
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 22
  • ???jsp.display-item.citation.isi??? 19
social impact