摘要
本文介绍了使用带约束多段多项式进行数据拟合的实用算法及软件。这种基于最小二乘法的方法比单个高阶多项式拟合更能刻画某些所需的局部特性。文中考虑了分段节点处及非分段节点处的三种等式约束,即函数值、斜率值及二阶导数值约束,可以满足数据拟合的实际需要。相应的计算机程序以 MS-FORTRAN4.0及 MASM 5.0混合写成人图交互及 Borland 风格菜单形式。应用用户友好程序设计思想,增强了普通数值计算程序的应用潜力。通过方便的人图交互确定合适的分段数、节点安排及各段多项式阶次以得到满意的拟合结果。最后给出了一个实际应用例子以表明本文算法及软件的实用性。
This paper introduced a practical method and programsfor data fitting by multi-segment polynomials with constraints.Basedon least squares method,this method can depict some relevant localproperties wanted and can overcome the disadvantages of least squaresfitting with one high degree polynomial.In this proposed method,onlythe equation constraints are considered such as functional value equationconstraints,tangent value equation constraints,second derivatives equa-tion constraints etc.Three kinds of equation constraints above mentionedare applied which may meet the practical data fitting requirements.Theformulae about the applied constraints are given.The computer programsare coded in automatic man-graphics interaction form and with theBorland style menu The compact software are implemented in MS-FORTRAN4.0 and MASM5.0 languages.The ideals of user-friendshipprogramming technique are employed to enlarge the applicable poten-tials of ordinary numerical computation routines.Through the readinessman-graphics interaction the proper number of segments,knot arrange-ment and degree of polynomials in each segment can be decided to getthe satisfatory fitting result.A practical application example is givenwhich demonstrates the effectiveness and usefulness ofthe method andthe software of this article.
关键词
最小二乘法
数据处理
软件
piecewise fitting
least squares method
constrained optimization
data processing
software engineering
