The induced dimension reduction (IDR) method of Sonneveld and van Gijzen [SIAM J. Sci. Comput 31(2008), pp. 1035-1062] is shown to be a Petrov-Galerkin (projection) method with a particular choice of left Krylov subspaces; these left subspaces are rational Krylov spaces. Consequently, other methods, such as BiCGStab and ML(s)BiCGStab, which are mathematically equivalent to some versions of IDR, can also be interpreted as Petrov-Galerkin methods. The connection with rational Krylov spaces inspired a new version of IDR, called Ritz-IDR, where the poles of the rational function are chosen as certain Ritz values. Experiments are presented illustrating the effectiveness of this new version.
V. Simoncini, D. B. Szyld (2010). Interpreting IDR as a Petrov-Galerkin method. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 32, 1898-1912 [10.1137/090774756].
Interpreting IDR as a Petrov-Galerkin method
SIMONCINI, VALERIA;
2010
Abstract
The induced dimension reduction (IDR) method of Sonneveld and van Gijzen [SIAM J. Sci. Comput 31(2008), pp. 1035-1062] is shown to be a Petrov-Galerkin (projection) method with a particular choice of left Krylov subspaces; these left subspaces are rational Krylov spaces. Consequently, other methods, such as BiCGStab and ML(s)BiCGStab, which are mathematically equivalent to some versions of IDR, can also be interpreted as Petrov-Galerkin methods. The connection with rational Krylov spaces inspired a new version of IDR, called Ritz-IDR, where the poles of the rational function are chosen as certain Ritz values. Experiments are presented illustrating the effectiveness of this new version.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
