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中文摘要：
引入非正规化的球谐函数，使用Clenshaw求和法不需要计算单个球谐函数值而直接计算级数和。将Clenshaw求和算法和标准向前列递推算法在计算时间上进行比较，并对两种方法计算的稳定性进行了数值分析，给出了数值模拟结果。通过数值计算得出了Clenshaw求和计算全球大地水准面差距的适用范围，为实现高精度大地水准面的计算提供借鉴。
英文摘要：
Based on the introduction of fully non-normalized spherical harmonics, Clenshaw summation does not need a single spherical harmonics calculation. We compared Clenshaw summation method with standard forward column method in the calculation of time and ana- lyzed the stability of these two methods by numerical tests. Then, we give the results of the tests. Finally, the applicability of geoid undulation computed based on Clenshaw summation method was discussed, which offers a reference for high-precision calculation of the geoid.
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