A new method is proposed to compute the eigenpairs of a parameter-dependent nonlinear eigenvalue problem. We first analyze the properties on the analytic perturbation of the invariant pair of a nonlinear eigenvalue problem and provide a method to compute the first-order and high-order derivatives of the invariant pair. On these grounds, the subspaces independent of the parameter and containing the approximations to the desired eigenvectors of a nonlinear eigenvalue problem are constructed. Then the desired eigenpairs of a nonlinear eigenvalue problem are obtained by projecting the parameter-dependent nonlinear eigenvalue problem to the generated subspaces. The errors of the computed eigenpairs are estimated. Finally, the efficiency of the proposed method is illustrated with some numerical examples.

中文翻译：

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参数相关非线性特征值问题的一种基于微扰的方法

提出了一种计算参数相关非线性特征值问题的特征对的新方法。我们首先分析了非线性特征值问题的不变对的解析摄动的性质，并提供了一种计算不变对的一阶和高阶导数的方法。基于这些理由，构建了独立于参数并包含非线性特征值问题的所需特征向量的近似值的子空间。然后通过将依赖于参数的非线性特征值问题投影到生成的子空间来获得非线性特征值问题的期望特征对。估计计算的特征对的误差。最后，通过一些数值例子说明了所提出方法的有效性。