1、解:(1)根据已给数据列均差表,如下均差表0.2 0.98 0.4 0.92 -0.30.6 0.81 -0.55 -0.6250.8 0.64 -0.85 -0.75 -0.2081 0.38 -1.3 -1.125 -0.625 -0.521则:P4(x)=0.98-0.3(x-0.2)-0.625(x-0.2)(x-0.4)-0.208(x-0.2)(x-0.4)( x-0.6)-0.521(x-0.2) (x-0.4)( x-0.6) ( x-0.8)(2)M0=M4=0,h0= h1= h2= h3=0.2, 1= 2= 3= 4=0.5 1= 2= 3=0.5，令 d0=2f0，
2、， =0，d 4=2f4， ， =0d1=6f(x0, x1, x2)=-7.5, d2=6f(x1, x2, x3)=-9.0d3=6f(x2, x3, x4)=-13.5则：=25.02504310M05.9.7在 MATLAB 中，输入下面程序，A=2 0 0 0 0;0.5 2 0.5 0 0;0 0.5 2 0.5 0;0 0 0.5 2 0.5;0 0 0 0.5 2b=0 -7.5 -9.0 -13.5 0;x=Ab解之得M0=0, M1=-3.244, M2=-2.0239, M3=-6.6603, M4=1.6651, 将 M0, M1, M2, M3, M4 代入表达式（6
3、.8）得到S(x)= 0.1,8).0(84.1)(42.3)8.0(3.1)(5. 623076580671 .,4.7.67.2 ,)()(9)2(33 Xxxxx在 MATLAB 中，输入下面程序，syms xf=0.98-0.3*(x-0.2)-0.625*(x-0.2)*(x-0.4)-0.208*(x-0.2)*(x-0.6)*(x-0.4)-0.521*(x-0.2)*(x-0.4)*(x-0.6)*(x-0.8);xx=0.2,0.4,0.6,0.8,1;yy=subs(f,x,xx)plot(xx,yy)hold onx=0.2 0.4 0.6 0.8 1.0;y=0.98 0.92 0.81 0.64 0.38;xx=0.2:0.01:1;y2=interp1(x,y,xx,spline); plot(x,y,o,xx,y2,-)得到下面图表:
