Computing Partial Spectra with Least-Squares Rational Filters
Computing Partial Spectra with Least-Squares Rational Filters
复制标题
DOI：
10.1137/16m1061965
复制
发表时间：
2016-09
期刊：
影响因子：
--
通讯作者：
Yuanzhe Xi;Y. Saad
中科院分区：
文献类型：
--
作者：
Yuanzhe Xi;Y. Saad
我们提出了一种基于子空间迭代与有理滤波相结合的计算埃尔米特矩阵部分谱的方法。与经典的有理滤波器来自柯西积分或统一近似的阶梯函数，我们采用最小二乘（LS）的观点设计过滤器。所提出的方法的目标之一是建立一个过滤器，将导致线性系统，更容易解决的迭代方法。所提出的LS滤波器的主要优点之一是它们的灵活性。因此，我们可以将极点放置在比上面提到的公式更一般的位置，并且我们还可以重复这些极点几次以获得更好的效率。这导致比现有方法更少数量的所需极。因此，当使用直接求解器时，因子分解成本降低，并且该方案对于迭代求解器也是有益的。本文讨论了求解滤波后的线性方程组的迭代格式。
We present a method for computing partial spectra of Hermitian matrices, based on a combination of subspace iteration with rational filtering. In contrast with classical rational filters derived from Cauchy integrals or from uniform approximations to a step function, we adopt a least-squares (LS) viewpoint for designing filters. One of the goals of the proposed approach is to build a filter that will lead to linear systems that are easier to solve by iterative methods. Among the main advantages of the proposed LS filters is their flexibility. Thus, we can place poles in more general locations than with the formulations mentioned above, and we can also repeat these poles a few times for better efficiency. This leads to a smaller number of required poles than in existing methods. As a consequence, factorization costs are reduced when direct solvers are used and the scheme is also beneficial for iterative solvers. The paper discusses iterative schemes to solve the linear systems resulting from the filtered s...