An error analysis of two related quadrature methods for computing zeros of analytic functions
An error analysis of two related quadrature methods for computing zeros of analytic functions
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DOI：
10.1016/s0377-0427(02)00724-0
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发表时间：
2003-03
影响因子：
2.4
通讯作者：
T. Sakurai;P. Kravanja;H. Sugiura;M. Barel
中科院分区：
文献类型：
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作者：
T. Sakurai;P. Kravanja;H. Sugiura;M. Barel
我们提出了两种相关求积方法（Delves–Lyness 方法及其由 Kravanja、Sakurai 和 Van Barel 进行的修改）的误差分析，用于计算位于单位圆内的解析函数的所有零点。如果通过单位圆上的梯形规则计算积分，我们会考虑前向和后向近似误差。与 Delves-Lyness 方法相反，单位圆内零点产生的正交误差不会影响 Kravanja 等人方法的结果。数值实验说明了我们的主要结果。
We present an error analysis for two related quadrature methods (the Delves–Lyness method and its modification by Kravanja, Sakurai and Van Barel) for computing all the zeros of an analytic function that lie inside the unit circle. We consider the forward as well as the backward approximation error in case the integrals are computed via the trapezoidal rule on the unit circle. Contrary to the Delves–Lyness method, the quadrature error that arises from the zeros located inside the unit circle does not affect the results of the approach of Kravanja et al. Numerical experiments illustrate our main results.