函数的分段有理二次B样条插值  

RATIONAL QUADRATIC B-SPLINE INTERPOLATION OF FUNCTION SEGMENTS

作　　者：梁锡坤[1] 

机构地区：[1]杭州师范大学杭州国际服务工程学院,杭州310012

出　　处：《高等学校计算数学学报》2012年第1期52-60,共9页Numerical Mathematics A Journal of Chinese Universities

摘　　要：科学和工程计算中，函数的近似表示一直是一个重要课题．近似方法一般可归结为插值、逼近和拟合三种基本类型，经历长期发展，函数逼近方法十分丰富．诸如Taylor公式、Lagrange-Newton插值、多项式样条方法、最佳平方逼近、最小二乘拟合、连分式插值、有理样条表示等等，它们在函数近似表示方面均发挥着不同程度的作用．Based on the proper segmentation of complicated functions, the trian- gle convex hull of functions segment is introduced. We propose a scheme of control polygon determination by the tangent of the endpoints of the segment intervals. The algorithm of the segment rational quadratic B-spline interpolation of compli- cated functions is discussed in details. The interpolation keeps many important geometric features of the original function such as convexity, monotonicity and G1 continuity. The numerical experiments show that the algorithm provides an effi- cient approach to approximate representation of complicated functions.

关 键 词：B样条插值 有理样条 函数 TAYLOR公式 Newton插值 最小二乘拟合 分段 最佳平方逼近 

分 类 号：O241.3[理学—计算数学]