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A parallel way for computing eigenvector sensitivity of asymmetric damped systems with distinct and repeated eigenvalues

机译：计算具有不同和重复特征值的非对称阻尼系统特征向量灵敏度的并行方法

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摘要

A high efficient method is proposed for computing the eigensolution derivatives of asymmetric damped systems with distinct and repeated eigenvalues. A new normalization for the left eigenvectors is proposed, from which a new form of the constraints of the left eigenvector sensitivities can be derived. The aim of this paper is to show how to compute the left and right eigenvector derivatives separately and independently such that those can be computed in a parallel way. In addition, the calculation of eigenvalue sensitivity of N damped asymmetric systems with repeated eigenvalues is derived. The proposed method is well-conditioned since the components of coefficient matrices are all of the same order of magnitude. The method is simple, compact and easy to be implemented on computers. Three numerical examples are used to illustrate the application, accuracy and efficiency of the proposed method.
机译：提出了一种计算特征值重复且不对称的非对称阻尼系统本征解导数的高效方法。提出了一种新的左特征向量归一化方法，由此可以导出左特征向量敏感度约束的一种新形式。本文的目的是展示如何分别和独立地计算左和右特征向量导数，从而可以并行地计算它们。此外，推导了具有重复特征值的N个阻尼非对称系统的特征值灵敏度计算。所提出的方法条件良好，因为系数矩阵的分量都处于相同的数量级。该方法简单，紧凑并且易于在计算机上实现。通过三个数值例子说明了该方法的应用，准确性和效率。

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