Abstract

To solve a nonlinear eigenvalue problem we develop algorithms which compute zeros of \(\det A(\lambda ) = 0\). We show how to apply third order iteration methods for that purpose. The necessary derivatives of the determinant are computed by algorithmic differentiation. Since many nonlinear eigenvalue problems have banded matrices we also present an algorithm which makes use of their structure.

中文翻译：

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求解非线性特征值问题的新算法

摘要

为了解决非线性特征值问题，我们开发了计算\(\det A(\lambda ) = 0\) 的零点的算法。我们展示了如何为此目的应用三阶迭代方法。通过算法微分计算行列式的必要导数。由于许多非线性特征值问题具有带状矩阵，因此我们还提出了一种利用其结构的算法。