三次样条构造的伪逆解法  

Pseudoinverse solution to construction of cubic splines

作　　者：张雨浓[1] 劳稳超[1] 肖林[1] 陈宇曦[1] 

机构地区：[1]中山大学信息科学与技术学院,广州510006

出　　处：《计算机应用研究》2014年第2期590-592,607,共4页Application Research of Computers

基　　金：国家自然科学基金资助项目(61075121);国家教育部高等学校博士学科点专项科研基金博导类课题资助项目(20100171110045)

摘　　要：为了提高三次样条构造的可行性,基于矩阵的伪逆方法,提出一种不依赖额外约束条件的三次样条构造的伪逆解法。该解法通过求解出三次样条二阶导数的最小范数解,从而较好地构造出三次样条函数。理论分析及数值实验结果表明该三次样条构造的伪逆解法具有简单、有效等特点。综合分析各种构造解法的性质,对各种三次样条构造解法进行归类比较,为在实际工程计算应用中选择合适的三次样条构造解法提供了指导方向。In order to promote the feasibility of the construction of cubic splines, this paper presented a novel pseudoinverse- based construction method （PCM） to construct the cubic spline function effectively. Without using endpoint-constraint condi- tions, this method obtained the solution of the second-order derivatives of the cubic spline that was closest to the origin, name- ly the minimum norm solution. Theoretical analysis and numerical experiments highlight the efficacy of the PCM. For better understanding, it further studied and investigated the characteristics of various construction methods. In this way, it provided guidelines for choosing suitable methods to construct cubic splines in practical applications of engineering calculation.

关 键 词：三次样条函数 插值 端点约束条件 伪逆 最小范数解 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]