累积两点信息的有理逼近RALND的改进

AN IMPROVEMENT FOR THE RATIONAL APPROXIMATION RALND AT ACCUMULATED TWO-POINT INFORMATION

文献[1l提出了分子分母皆为线性函数的多元有理逼近(Rational Approximation with Linear Numerator and Denominator,RALND),满意地求了非线性方程组的解和数学规划最优解,为了克服RALND的不足,使之更好地发挥作用,本文试图改进该逼近:(1)提出了更合理地筛选有理逼近解的方法;(2)证明了该逼近的单调性;(3)对于原函数在当前点与前次迭代点连线方向上方向导数符号相反的情况,分别提出了迭代求有理逼近和构造在当前点与估算点连线方向上相应的方向导数符号相同的近似有理逼近的方法;(4)提出了一个非单调的有理逼近函数;(5)通过数值计算验证了本文提出的有理逼近是有效和可行的.

A rational approximation with linear numerator and denominator （RALND） in ref- erences [1] was proposed to be applied in solving nonlinear equations and mathematical programming satisfactorily. This paper attempts to improve the approximation in order to overcome RALND＇s lack to play its role preferably： （1） A method of selecting the more prop- er solution of rational approximations is presented. （2） The rational approximation is proven to be a monotonic function. （3） For having opposite signs of two directional derivatives a- long the direction connecting the current iterative point and the previous iterative point of an original function, we propose an iterative method of solving its rational approximation and an approximate method to construct a rational function with same signs corresponding directional derivatives along the direction connecting the current iterative point and another estimate point, respectively. （4） A non-monotonic rational approximation function is pre- sented. （5） Numerical experimental results show the validity and feasibility of the rational approximation of this paper.