实验一三次样条插值的三弯矩法

1、实验一 三次样条插值的三弯矩法一、实验目的用三次样条插值的三弯矩法,编制第一与第二种边界条件的程序.已知数据,及边界条件,编程计算的三次样条插值函数.具体要求为:输出用追赶法解出的弯矩向量及的值;画出的图形,图形中描出插值点及分别用o和*标记.二、实验原理（1）由xk-ykk=0,1,2,n,按公式Skx=Mk-1xk-xhk+Mkx-xk-1hk,hk=xk-xk-1k=hk+1hk+hk+1,k=hkhk+hk+1, dk=6hk+hk+1yk+1-ykhk+1-yk-yk-1hkd0=60h1y1-y0h1-y0+21-0y0,dn=6nhnyn-yn-yn-1hn+21-nyn求出hk

2、,k,k,dk.（2）由边界条件确定0，d0和n,dn。（3）用追赶法解线性方程组2 01 2 1 1 2 2 n-22n-2n-12 n-1 n2 M0M1M2Mn-2Mn-1Mn=d0d1d2dn-2dn-1dn求出M0,M1,M2,Mn（4）由Skx=Mk-1xk-x36hk+Mkx-xk-136hk+xk-xhkyk-1-Mk-16hk2+x-xk-1hkyk-Mk6hk2确定Skx,得到S(x).三、实验结果所用数据:x=-5,-3.8884,-3.0142,-2.3216,-1.7433,-1.3771,-1.1318,-0.86821,-0.58598,-0.4314,-0.02

3、93,0.4314,0.58598,0.86821,1.1318,1.3771,1.7433,2.1242,2.3216,3.0142,3.8884,5;y=0.03846,0.06204,0.09915,0.1565,0.2476,0.3453,0.4384,0.5702,0.7444,0.8431,0.9991,0.8431,0.7444,0.5702,0.4384,0.3453,0.2476,0.1814,0.1565,0.09915,0.06204,0.03846;d2s1=0.0084;d2sn=0.0084;%第二种边界条件t=-4.166,-3.233,-2.495,-1.888

4、,-1.469,-1.193,-0.9341,-0.6565,-0.47,-0.1298,0.3162,0.5473,0.7977,1.066,1.316,1.652,2.029,2.272,2.841,3.67; 用追赶法求得的弯矩量为要计算的20个节点出的值为M0=0.0084M1=0.M2=0.M3=0.10891M4=0.2393M5=0.38381M6=0.48683M7=0.50559M8=0.M9=-0.55789M10=-2.2251M11=-0.64145M12=0.M13=0.50104M14=0.48825M15=0.3828M16=0.24171M17=0.14866M

5、18=0.11118M19=0.M20=0.M21=0.0084S(-4.166)=0.S(-3.233)=0.S(-2.495)=0.13838S(-1.888)=0.219S(-1.469)=0.3167S(-1.193)=0.41267S(-0.9341)=0.53401S(-0.6565)=0.69895S(-0.47)=0.81911S(-0.1298)=0.9833S(0.3162)=0.90801S(0.5473)=0.76957S(0.7977)=0.61123S(1.066)=0.46809S(1.316)=0.36609S(1.652)=0.26819S(2.029)=0.

6、1954S(2.272)=0.16229S(2.841)=0.11017S(3.67)=0.要计算的20个节点出的一阶导数值为:要计算的20个节点出的二阶导数值为:dS(-4.166)=0.dS(-3.233)=0.dS(-2.495)=0.dS(-1.888)=0.18189dS(-1.469)=0.29464dS(-1.193)=0.40603dS(-0.9341)=0.53267dS(-0.6565)=0.63919dS(-0.47)=0.63031dS(-0.1298)=0.25502dS(0.3162)=-0.51127dS(0.5473)=-0.6502dS(0.7977)=-0.

7、59727dS(1.066)=-0.46734dS(1.316)=-0.35247dS(1.652)=-0.2376dS(2.029)=-0.15484dS(2.272)=-0.11968dS(2.841)=-0.dS(3.67)=-0.d2S(-4.166)=0.d2S(-3.233)=0.04067d2S(-2.495)=0.d2S(-1.888)=0.20668d2S(-1.469)=0.34754d2S(-1.193)=0.46113d2S(-0.9341)=0.5009d2S(-0.6565)=0.18747d2S(-0.47)=-0.39823d2S(-0.1298)=-1.8084d2S(0.3162)=-1.0374d2S(0.5473)=-0.d2S(0.7977)=0.40029d