大学数值计算方法题目答案

1、大学数值计算方法题目答案 数值计算方法 黄云清编 数值计算方法 project ii solutions: 1.give the formula of the following methods: langerange interpolation、piecewise linear langerange interpolation and cubic spline interpolation (1)langerange interpolation formula： ln(x) yili(x), i 0n li(x) (x x0).(x xi 1)(x xi).(x xn),i 0,1,.,n(x

2、i x0).(xi xi 1)(xi xi 1).(xi xn) 其中基函数满意： 1,i j li(xj) 0,i j,i,j 0,1,.n piecewise linear langerange interpolation formula： in yjlj(x), j 0n x xj 1,xj 1 x xj x xj 1 j x xj 1lj(x) ,xj x xj 1 xj x 0,x cubic spline interpolation： s(x) si(x),x xi 1,xi ,i 1,.,n si(x) aix bix cix di32 其中ai,bi,ci,di为待定系数，共4

3、n个，且满意条件： 数值计算方法 黄云清编 si(xi) si 1(xi) si'(xi) si' 1(xi),i 1,2,.,n 1， '''' si(xi) si 1(xi) s''(x0) s''(xn) 0 (2) give matlab or c program langerange函数文件： function y=lagr(x0,y0,x) n=length(x0);m=length(x); for i=1:m z=x(i); s=0; for k=1:n p=1; for j=1:n if j=k p

4、=p*(z-x0(j)/(x0(k)-x0(j); end end s=p*y0(k)+s; end y(i)=s; 数值计算方法 黄云清编 end 程序： x0=2021.01,2021.02,2021.03,2021.04,2021.05,2021.06,2021.07,2021.08,2021.09,2021.10,2021.11,2021.12,2021.01,2021.02,2021.03,2021.04,2021.05,2021.06,2021.07,2021.08,2021.09,2021.10,2021.11,2021.12,2021.01,2021.02,2021.03,20

5、21.04,2021.05,2021.06,2021.07,2021.08,2021.09,2021.10,2021.11,2021.12,2021.01,2021.02,2021.03,2021.04,2021.05,2021.06; y0=8.0668 8.0493 8.0035 8.0156 8.0152 8.0067 7.991 7.9733 7.9368 7.9032 7.8652 7.8238 7.7898 7.7546 7.739 7.7247 7.6704 7.633 7.5805 7.5753 7.5258 7.5805 7.4233 7.3676 7.2478 7.1601

6、 7.0752 7.2478 6.9724 6.8971 6.8376 6.8515 6.8307 6.8316 6.8286 6.8424 6.8382 6.8357 6.8341 6.8312 6.8345 6.8332; x=2021:0.1:2021; y1=lagr(x0,y0,x); y2=interp1(x0,y0,x); y3=spline(x0,y0,x); z=0*x; 数值计算方法 黄云清编 plot(x,z,x0,y0,'.',x,y1,'r',x,y2,'m',x,y3,'c') axis(2021 2021 -10 10) gtext('lagr') gt