Interpreting IDR as a Petrov--Galerkin Method
Interpreting IDR as a Petrov--Galerkin Method
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DOI：
10.1137/090774756
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发表时间：
2010-06
期刊：
影响因子：
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通讯作者：
V. Simoncini;D. Szyld
中科院分区：
文献类型：
--
作者：
V. Simoncini;D. Szyld
Sonneveld和货车Gijzen [SIAM J. Sci.计算，31（2008），pp. 1035-1062]是一个Petrov-Galerkin（投影）方法，具有特定的左Krylov子空间选择;这些左子空间是有理Krylov空间。因此，其他方法，如BiCGStab和ML（$s$）BiCGStab，在数学上等同于IDR的某些版本，也可以解释为彼得罗夫-伽辽金方法。与有理Krylov空间的联系启发了IDR的新版本，称为Ritz-IDR，其中有理函数的极点被选择为某些Ritz值。实验表明，这个新版本的有效性。
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.