关于样条数值微分和数值积分的进一步讨论  

Further Discussion on Numerical Differentiation and Numerical Integration Using Cubic Spline Function

作　　者：孙靖[1] 金花[1] 曹德欣[1] 

机构地区：[1]中国矿业大学理学院

出　　处：《中国矿业大学学报》2002年第1期103-106,共4页Journal of China University of Mining & Technology

摘　　要：进一步讨论样条数值微分和数值积分方法 .分别针对 型和 型三次样条在非等距节点分布的情况下 ,研究了各节点数据误差包括边界条件数据误差对样条数值微分和数值积分计算结果的影响 ,导出了相应的误差估计式 .结果表明 ,节点数据误差对样条数值微分的影响随着远离节点而衰减 ,对样条数值积分的影响是有界的 (在划分比有界的情况下 ) .此外还对样条数值积分的方法误差进行了讨论 ,导出了求积余项的估计式 .Under unequal distance nodes distribution, the effect of errors of both the boundary conditions and function value dates on numerical differentiation and numerical integration using cubic spline were discussed. The error estimate formulas were given. The results show that the effect of the error of a function value date on numerical differentiation at other nodes decreases with other nodes far from this one, and that round error of numerical integration is bounded when the ratio of division is bounded. And the estimate formulas of truncation error of numerical integration using cubic spline were proposed.

关 键 词：样条数值微分 数值积分 误差 边界条件 

分 类 号：O241.4[理学—计算数学]