The paper proves the quadratic convergence of the complex HZ method for solving the positive definite generalized eigenvalue problem. The proof is made for a general cyclic pivot strategy in the case of simple eigenvalues and for any wavefront pivot strategy in the case of simple or double eigenvalues. The proof is valid for the real HZ method. The preliminary numerical tests confirm the theoretical results.

中文翻译：

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关于正定广义特征值问题的复HZ方法的二次收敛

证明了复HZ法求解正定广义特征值问题的二次收敛性。对简单特征值情况下的一般循环枢轴策略和简单或双特征值情况下的任何波前枢轴策略进行了证明。该证明对真实 HZ 方法有效。初步数值试验证实了理论结果。