在多项式型变换下具有不变性的算法
On the Algorithms Invariant to Polynomial-Type Scaling
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摘要: 本文讨论根据较一般的目标函数模型(3)建立具有非线性尺度不变性的算法的理论依据。文献2研究了F(q)是二次函数的情形,我们可以把它看做是用q的二次函数逼近一般的F(q)。本文研究逼近F(q)的一般问题,对于用高阶多项式逼近和用低阶多项式分段逼近的两种策略,分别导出了计算ρK的解析表达式,并建立了相应的算法。Abstract: This paper discusses the algorithms invariant to nonlinear scaling for more general objective function model(3). The case of algorithms was studied in 2 when F(q) is a quadratic function. Here we study a more general problem - approximation F(q) with high-order polynomial and with piecewise low-order polynomial. The analytic formulas of ρK for both cases are derived and the corresponding algorithms are established.