Rational Krylov Algorithms for Nonsymmetric Eigenvalue Problems
Rational Krylov Algorithms for Nonsymmetric Eigenvalue Problems
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DOI：
10.1007/978-1-4613-9353-5_10
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发表时间：
1994
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影响因子：
--
通讯作者：
Axel Ruhe
中科院分区：
文献类型：
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作者：
Axel Ruhe
给出了求解非对称矩阵束特征值问题的有理Krylov算法。它是移位和逆Lanczos（或Arnoldi）算法的推广，其中在一次运行中使用几个移位。它计算一个正交基和一个小的Hessenberg铅笔。Hessenberg束的本征解给出了原束解的Ritz近似。当矩阵的因式分解并不比解的代价高得多时，有理Krylov是自然的选择，例如当使用多重网格算法来求解系统时。在一个变体中，在同一个起始向量上开始具有不同移位的几次迭代。这样的迭代可以并行执行，在p个处理器上的一次迭代中产生p度Krylov向量。模拟实验验证飞机结构的稳定性的方法。
The Rational Krylov algorithm for the nonsymmetric matrix pencil eigenvalue problem is described. It is a generalization of the shifted and inverted Lanczos (or Arnoldi) algorithm, in which several shifts are used in one run. It computes an orthogonal basis and a small Hessenberg pencil. The eigensolution of the Hessenberg pencil, gives Ritz approximations to the solution of the original pencil. Rational Krylov is the natural alternative when factorization of the matrix is not much more expensive than solution, as eg when a multigrid algorithm is used to solve systems.In one variant several iterations with different shifts are started on the same starting vector. Such iterations can be performed in parallel, yielding a p degree Krylov vector in one iteration on p processors. An analogy to a method of experimentally verifying stability of aircraft structures is shown.