有限Blaschke乘积构造的数值模型：具有预设不同临界点
A Numerical Model for the Construction of Finite Blaschke Products with Preassigned Distinct Critical Points
AI总结：
本文提出一种数值方法，用于构造具有预设不同临界点的有限Blaschke乘积，通过构建稀疏非线性方程组和临界点变换，验证了方法的效率和精度。
摘要：
我们提出了一种数值模型，用于确定具有n个预设不同临界点z₁,…,zₙ的有限Blaschke乘积，其阶数为n+1。Blaschke乘积在单位圆盘D的共形自守映射后置复合下唯一确定。所提方法基于构建稀疏非线性方程组，其中数据依赖被隔离到两个向量中，并对临界点进行某种变换。方法的效率和精度通过多个示例进行了说明。
英文摘要：
We present a numerical model for determining a finite Blaschke product of degree $n+1$ having $n$ preassigned distinct critical points $z_1,\dots,z_n$ in the complex (open) unit disk $\mathbb{D}$. The Blaschke product is uniquely determined up to postcomposition with conformal automorphisms of $\mathbb{D}$. The proposed method is based on the construction of a sparse nonlinear system where the data dependency is isolated to two vectors and on a certain transformation of the critical points. The efficiency and accuracy of the method is illustrated in several examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
