论文标题
特征向量非线性的隐式算法
Implicit algorithms for eigenvector nonlinearities
论文作者
论文摘要
我们研究并得出非线性特征值问题的算法，其中系统矩阵取决于特征向量或几个特征向量（或它们相应的不变子空间）。算法是从隐式观点得出的。更确切地说，我们以下一个迭代的方式更改牛顿更新方程式，不仅在更新方程中出现线性。虽然，更新方程式的修改使我们展示了如何明确计算相应的迭代方法。因此，我们可以使用明确的过程来执行隐式方法的步骤。在某些情况下，这些程序涉及标准特征值问题的解决方案。我们提出了两种修改，其中一种修改直接导致了一个公认的方法（自洽场迭代），而另一种方法是我们的知识新知识，并且具有一些有吸引力的属性。提供收敛理论以及几个模拟，以说明算法的特性。
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit viewpoint. More precisely, we change the Newton update equation in a way that the next iterate does not only appear linearly in the update equation. Although, the modifications of the update equation make the methods implicit we show how corresponding iterates can be computed explicitly. Therefore we can carry out steps of the implicit method using explicit procedures. In several cases, these procedures involve a solution of standard eigenvalue problems. We propose two modifications, one of the modifications leads directly to a well-established method (the self-consistent field iteration) whereas the other method is to our knowledge new and has several attractive properties. Convergence theory is provided along with several simulations which illustrate the properties of the algorithms.
