An Inexact Cayley Transform Method For Inverse Eigenvalue Problems
An Inexact Cayley Transform Method For Inverse Eigenvalue Problems
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DOI：
10.1088/0266-5611/20/5/022
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发表时间：
2004-10
期刊：
影响因子：
2.1
通讯作者：
Zhengjian Bai;R. Chan;B. Morini
中科院分区：
文献类型：
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作者：
Zhengjian Bai;R. Chan;B. Morini
凯莱变换法是一种求解特征值反问题的类牛顿方法。如果问题很大，可以通过迭代方法求解雅可比方程。然而，迭代方法通常过度解决问题，因为它们需要的（内部）迭代远远超过牛顿（外部）迭代收敛所需的迭代。在本文中，我们开发了一个不精确版本的凯莱变换方法。我们的方法可以减少过度求解的问题，它提高了效率方面的确切版本。我们表明，我们的方法的收敛速度是超线性的，可以得到一个很好的权衡所需的内部和外部迭代。
The Cayley transform method is a Newton-like method for solving inverse eigenvalue problems. If the problem is large, one can solve the Jacobian equation by iterative methods. However, iterative methods usually oversolve the problem in the sense that they require far more (inner) iterations than is required for the convergence of the Newton (outer) iterations. In this paper, we develop an inexact version of the Cayley transform method. Our method can reduce the oversolving problem and it improves the efficiency with respect to the exact version. We show that the convergence rate of our method is superlinear and that a good tradeoff between the required inner and outer iterations can be obtained.