分段线性插值函数的编程实现摘要

《分段线性插值函数的编程实现摘要》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、分段线性插值函数的编程实现分段线性插值函数的编程实现摘要在代数插值过程中，人们为了获得较好的近似效果，通常情况下是增加插值节点数.由于二次插值比线性插值近似效果好，因此容易错误地认为插值多项式次数越高越好.事实上,随着插值节点的增多，插值多项式不一定收敛到被插值函数.通过分段低次插值或样条插值可以得到较好的近似逼近函数，分段低次插值具有公式简单、运算量小、稳定性好、收敛性有保证等优点.随着子区间长度h取得足够小，分段低次插值总能满足所要求的精度.因此分段低次插值应用十分广泛.分段线性插值是分段低次插值中常见的方法之一，在本文中对在(-

2、5，5)上进行分段线性插值，取不同节点个数，得到不同分段线性插值函数.并用MATLAB编写分段线性插值函数，最后比较用不同节点数所得插值函数与真实函数的误差，从而得出节点数与插值效果的关系.关键字:线性插值;分段低次插值;分段线性插值函数;MATLAB软件分段线性插值函数的编程实现USINGPROGRAMMINGTOACHIEVETHEPIECEWISELINEARINTERPORATIONFUNCTIONABSTRACTIntheprocessofalgebrainterpolation,peopletypicallyincreas

3、etheinterpolationnodenumberinordertogetabetterapproximateresult.Astheresultcalculatedbyquadraticinterpolationisbetterthanthesameaspectbylinearinterpolation,itiswronglythoughtthatthehigherpowerofinterpolationthebettertheresultis.Infact,withtheincreaseofthenumberofnodeint

4、erpolationmethod,interpolationpolynomialisnotconvergentasinterpolationfunction.Itcangetmuchbetterapproximationfunctionthroughthepiecewiselowpowerofinterpolationorsplineinterpolation.Piecewiselowpowerofinterpolationiscomparablysimpleandthestabilityandtheconvergencecanbeg

5、uaranteed.Asthelengthhofthesubintervalapproachestozero,piecewiselowpowerinterpolationcanmeettherequiredaccuracy.Thismethodisusedwidely.Piecewiselinearinterpolationisoneofthetypicalmethodsofpiecewiselowpowerofinterpolation,inthisessay,wewillconductlinearinterpolationfrom

6、(-5,5)bydifferentnodenumbernandrelativepiecewiselinearinterpolationfunctions.Then,wewillprogrammelinearinterpolationbymatlabandcomparetheerrorbetweentheresultderivedfromlinearinterpolationandrealfunction.Themethodisusedtotesttherelationshipbetweendifferentlengthsandrela

7、tiveresultsofinterpolation.Keywords:linearinterpolation;piecewiselowpowerofinterpolation;piecewiselinearinterpolationfunction;MATLABsoftware分段线性插值函数的编程实现目录1问题的提出........................................................12理论基础...............................................

8、.........13编程过程..........................................................34结果分析...............................