Matlab程序三次样条插值函数

1、已知一组数据点，编写一程序求解三次样条插值函数满足 并针对下面一组具体实验数据0.250.30.390.450.530.50000.54770.62450.67080.7280求解，其中边界条件为.解：Matlab计算程序为：clearclcx=0.25 0.3 0.39 0.45 0.53y=0.5000 0.5477 0.6245 0.6708 0.7280n=length(x);for i=1:n-1 h(i)=x(i+1)-x(i);endfor i=1:n-2 k(i)=h(i+1)/(h(i)+h(i+1); u(i)=h(i)/(h(i)+h(i+1);endfor i=1:n-

2、2 gl(i)=3*(u(i)*(y(i+2)-y(i+1)/h(i+1)+k(i)*(y(i+1)-y(i)/h(i);endg0=3*(y(2)-y(1)/h(1);g00=3*(y(n)-y(n-1)/h(n-1);g=g0 gl g00;g=transpose(g)k1=k 1;u1=1 u;Q=2*eye(5)+diag(u1,1)+diag(k1,-1)m=transpose(Qg)syms X;for i=1:n-1p1(i)=(1+2*(X-x(i)/h(i)*(X-x(i+1)/h(i)2*y(i);p2(i)=(1-2*(X-x(i+1)/h(i)*(X-x(i)/h(i)

3、2*y(i+1);p3(i)=(X-x(i)*(X-x(i+1)/h(i)2*m(i);p4(i)=(X-x(i+1)*(X-x(i)/h(i)2*m(i+1);p(i)=p1(i)+p2(i)+p3(i)+p4(i);p(i)=simple(p(i);ends1=p(1)s2=p(2)s3=p(3)s4=p(4)for k=1:4 for z=x(k):0.001:x(k+1) q=eval(subs(p(k),'X','z'); plot(z,q,'b') hold on endendgrid onlegend('È

4、3;´ÎÑùÌõÇúÏß')title('²åÖµ')xlabel('x')ylabel('p')计算结果为：s1 = -(705394867539368680*X3 - 529046150654530286*X2 + 23087199381998953*X - 40023205577025431)/112589990684262400s2 =(257361898089296225*X3)/13679

5、6838681378816 - (160081743506404901*X2)/60798594969501696 + (404209705972252727*X)/202661983231672320 + 429142243010323951/3166593487994880000 s3 =- (3495912536773825*X3)/7599824371187712 + (1437374409830143*X2)/13510798882111488 + (10427488839800859*X)/11258999068426240 + 12358231431982259943/45035996273704960000 s4 =(38626753769033575*X3)/18014398509481984 - (245666153971053021*X2)/72057594037927936 + (3614707928905781673*X)/144