基于Clenshaw技术计算大地水准面差距的快速算法

随着超高阶重力场位模型的建立与精化,其计算效率也逐渐凸显起来.本文比较了Clenshaw算法和标准向前列递推算法的适用性,并分析了Clenshaw求和计算全球大地水准面差距的适用范围.在Clenshaw求和技术基础上,进行如下算法改进:将球谐函数级数和的形式以矩阵形式替代,算法运算过程中以向量化计算代替循环计算.在计算前360阶、420阶、480阶、……、直至前1500阶的大地水准面差距时,改进后的Clenshaw算法要比改进前算法的运算耗时减少了三分之一左右,也就是运算效率至少提升了33%.

Fast algorithm for calculating geoid undulation based on Clenshaw technique

With the establishment and elaboration of the ultra-highdegree gravitational field model,the calculation efficiency of the gravity field parameters becomes increasingly prominent.The paper compares the applicability of Clenshaw algorithm with that of the standard forward column algorithm by the first relative numerical accuracy,and analyzes the applicable interval of Clenshaw summation to calculate the global geoid undulation.On the basis of Clenshaw summation technology,the algorithm is improved as follows:the form of the series sum of spherical harmonic function is replaced by matrix form,and vectorization calculation is used instead of cycle calculation in the process of algorithm operation.In the calculation of the first 360 degrees,420 degrees,480 degrees,…,until the geoid undulation of the first 1500 degrees,the operation time of the improved Clenshaw algorithm is about one-third less than that of the unimproved algorithm,that is,the operation efficiency is improved by at least 33%.