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1、解:(1)根据已给数据列均差表,如下均差表0.20.980.40.92-0.30.60.81-0.55-0.6250.80.64-0.85-0.75-0.20810.38-1.3-1.125-0.625-0.521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，=0，d4=2f4，=0 d1=6f(x0,
2、 x1, x2)=-7.5, d2=6f(x1, x2, x3)=-9.0 d3=6f(x2, x3, x4)=-13.5则：=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（6.8）得到S(x)=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:
