Tracking poles and representing Hankel operators directly from data
Tracking poles and representing Hankel operators directly from data
复制标题
直接从数据跟踪极点并代表 Hankel 算子
DOI：
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
Nicholas Young
中科院分区：
文献类型：
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作者：
J. Helton;P. Spain;Nicholas Young
摘要我们提出并分析了一种估计函数G的单位圆T附近极点的方法，该函数G的值在T上的点的网格上给出：我们给出了执行这种估计的算法，并证明了收敛定理。该方法是通过考虑G在T上的绝对值的峰值来确定估计的相位，然后通过一阶有理函数在一个小圆弧上寻找G的最佳L2拟合来估计模。这些极点估计导致构造L2的基，该基非常适合于符号为G的Hankel算子的数值表示，从而适合于Nehari问题的数值解（计算相对于L ∞范数的G的最佳H ∞解析逼近），如[HY]中所分析的。我们提出了这些算法的数值试验的结果。
SummaryWe propose and analyse a method of estimating the poles near the unit circleT of a functionG whose values are given at a grid of points onT: we give an algorithm for performing this estimation and prove a convergence theorem. The method is to identify the phase for an estimate by considering the peaks of the absolute value ofG onT, and then to estimate the modulus by seeking a bestL2 fit toG over a small arc by a first order rational function. These pole estimates lead to the construction of a basis ofL2 which is well suited to the numerical representation of the Hankel operator with symbolG and thereby to the numerical solution of the Nehari problem (computing the bestH∞, analytic, approximation toG relative to theL∞ norm), as analysed in [HY]. We present the results of numerical tests of these algorithms.