改进的超越函数分段线性逼近方法

针对超越函数计算中所采用的分段线性逼近算法存在的无法提前确定精度及部分区间资源浪费的问题，提出一种改进的分段线性逼近超越函数算法。该算法由预定义的逼近区间端点计算出用于逼近的线性函数，根据被逼近函数的凹凸性对所计算线性函数进行调整，在此基础上计算出预定义逼近区间内调整后函数与被逼近函数之间的最大误差；按照所需精度的要求，自动调整逼近区间，通过该过程的迭代，获得了较少分段次数。算法结果在Matlab上进行仿真，仿真结果表明，所提算法的分段数相比等分法减少了60%。所提算法在保证精度的前提下，降低了查找表（LUT）的资源消耗。

Improved method of transcendental function piecewise linear approximation

When the transcendental function is used in the calculation of the piece-wise linear approximation algorithm, the accuracy can not be determined in advance and part of interval resources are wasted. In order to solve the problems, an improved piece-wise linear approximation algorithm of transcendental function was proposed. The proposed algorithm calculated a linear approximation function with predefined interval endpoints and adjusted the function by the concave of the function to be approximated and then calculated the maximum error between the function adjusted and the function to be approximated. The approximation intervals would be adjusted automatically based on the precision requirement and a fewer number of segments would be obtained by such iterative process. The proposed algorithm was simulated in Matlab. The simulation results show that the number of segments of the proposed algorithm is reduced by 60% compared with the equal division method. Thus, the proposed algorithm can reduce the resource consumption of the Look Up Table (LUT) greatly on the premise of guaranteeing accuracy.