实验一--三次样条插值的三弯矩法

1、实验、实验目的三次样条插值的三弯矩法?- ?-1?, ?= ?- ?-1? ? ?+1 ? ?= ?匚1,?=?+1?=(仝空-?)?+? ?+1 '?+1?cc ?6? ?0/ / /?= # (非-?) + 2(1 - ?)?, ? =?16?云(?论?-1) +?2(1 - ?)?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数据Xi, yif(Xi), i 0,L ,n及边界条件 y(k)(Xj),j 0,n,k 1,2 ,编程计算 f(x)的三次样条插值函数S(x).具体要求为：输出用追赶法解出的弯矩向量M Mo,L ,Mn及 S(k)(ti), i 0,L ,m,

2、k 0,1,2 的值;画出 y S(x)的图形,图形中描出插值点(x,yj及(ti,s(tj)分别用o'和'*'标记.实验原理(1)由(?- ?)(?= 0,1,2,?,按公式?- ?孜？ = ?-1 +? ?(2)(3)(4)求出？,?i,?3,?由2?3?2?2?2? =: ?-22?-2?-2?-2?-12?-1?-1?-1? 2?(?-?= ?-1?3+ '6? ? ?-1 + (?- ?-1 )3?-?+6? ?，1 ?-一？?？? 6.?-1 -?-1 2-V?2求出？? ? ? ?由边界条件确定?, ?和? ?= 用追赶法解线性方程组确定?(?,得

3、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,-0.0293,0.4314,0.58598,0.86821,1.1318,1.3771,1.7433,2.1242,2.3216,3.01 42,3.8884,5;y=0.03846,0.06204,0.09915,0.1565,0.2476,0.3453,0.4384,0.5702,0.7444,0.8431,0.9991,0.8431,0.7444,0.5702,0.4384,0.3453,0.24

4、76,0.1814,0.1565 ,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,-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=0.0084S(-4.166)=0.054449M1=0.019204S(-3.233)=0.087288M2=0.0478

5、36S(-2.495)=0.13838M3=0.10891S(-1.888)=0.219M4=0.2393S(-1.469)=0.3167M5=0.38381S(-1.193)=0.41267M6=0.48683S(-0.9341)=0.53401M7=0.50559S(-0.6565)=0.69895M8=0.081512S(-0.47)=0.81911M9=-0.55789S(-0.1298)=0.9833M10=-2.2251S(0.3162)=0.90801M11=-0.64145S(0.5473)=0.76957M12=0.097766S(0.7977)=0.61123M13=0.5

6、0104S(1.066)=0.46809M14=0.48825S(1.316)=0.36609M15=0.3828S(1.652)=0.26819M16=0.24171S(2.029)=0.1954M17=0.14866S(2.272)=0.16229M18=0.11118S(2.841)=0.11017M19=0.047302S(3.67)=0.069093M20=0.019321M21=0.0084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)=0.024928d2S(-4.166)=0.016506dS(-3.233)=0.049505d

7、2S(-3.233)=0.04067dS(-2.495)=0.095911d2S(-2.495)=0.093623dS(-1.888)=0.18189d2S(-1.888)=0.20668dS(-1.469)=0.29464d2S(-1.469)=0.34754dS(-1.193)=0.40603d2S(-1.193)=0.46113dS(-0.9341)=0.53267d2S(-0.9341)=0.5009dS(-0.6565)=0.63919d2S(-0.6565)=0.18747dS(-0.47)=0.63031d2S(-0.47)=-0.39823dS(-0.1298)=0.25502d2S(-0.1298)=-1.8084dS(0.3162)=-0.51127d2S(0.3162)=-1.0374dS(0.5473)=-0.6502d2S(0.5473)=-0.087206dS(0.7977)=-0.59727d2S(0.7977)=0.40029dS(1.066)=-0.46734d2S(1.066)=0.49144dS(1.316)=-0.35247d2S(1.316)=0.40907dS(1.652)=-0.2376d2S(1.652)=0.27689dS(2.029)=-0.15484d2S