确定Fourier展开式最佳截断项数的探讨

THE DETERMINATION OF THE OPTIMUM NUMBER OF TRUNCATED TERMS OF FOURIER EXPANSION AND NUMERICAL EXPERIMENTS

摘要: 本文用理论估计及数值实验两种方法研究了有限调和分析中考滤资料误差情况下如何确定Fourier展开式最佳截断项数的问题。理论估计表明最佳截断项数与物理量本身的变化及资料的误差有关。数值实验的结果证实了这一点。

Abstract: With data errors the optimum number of truncated terms of Fourier expansion is determined. According to the theoretical estimate the optimum number is related to data variation and their errors. The computations of the numerical experiments are in agreement with the theoretical results.