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1、数值试验题2,2.1 编制分段线性插值和分段三次Hermite插值程序，对被插函数 插值区间 ，分成10等分，求分段线性插值函数在各节点间中点处的值，并画出分段线性插值函数和 的图形。,下面6张是第1题,x=-4.5,-3.5,-2.5,-1.5,-0.5,0.5,1.5,2.5,3.5,4.5;f(x) ans = Columns 1 through 7 0.0486 0.0794 0.1500 0.3500 0.7500 0.7500 0.3500 Columns 8 through 10 0.1500 0.0794 0.0486,x=-5,-4,-3,-2,-1,0,1,2,3,4,5;
2、y= 0.0385,0.0588,0.1000,0.2000,0.5000,1.0000,0.5000,0.2000,0.1000,0.0588,0.0385;plot(x,y) ,画图命令如下：,图形如下：,下面6张是第2题,function Sanciyangtiao( X, Y, a, b ) % a = f(1), b = f(n) n = length( X ); for i = 1 : n-1 h(i) = X(i+1)-X(i); end for j = 2 : n-1 u(j) = h(j-1)/( h(j-1) + h(j) ); t(j) = 1 - u(j); d(j)
3、= 6*( (Y(j+1) - Y(j)/h(j) - (Y(j) - Y(j-1)/h(j-1) )/( h(j-1) + h(j) ); end t(1) = 1; u(n) = 1; d(1) = 6/h(1)*( (Y(2)-Y(1)/h(1) - a ); d(n) = 6/h(n-1)*( b - (Y(n)-Y(n-1)/h(n-1); for i = 1 : n A(i,i)=2; A(1,2)=1; A(n,n-1)=1; for j = 2 : n-1 A(j,j-1)=u(j); A(j,j+1)=t(j); if abs(i-j)1 A(i,j) = 0; end en
4、d end,程序(1)(a),D = d; N = AD; M = N; for i = 1 : n-1 H(i)=(M(i+1)-M(i)/(6*h(i); I(i)=(M(i)*X(i+1)-M(i+1)*X(i)/(2*h(i); J(i)=(M(i+1)*X(i)2-M(i)*X(i+1)2+2*(Y(i+1)-Y(i)+h(i)2/3*(M(i)-M(i+1)/(2*h(i); K(i)=(M(i)*X(i+1)3-M(i+1)*X(i)3+(6*Y(i)-M(i)*h(i)2)*X(i+1)-(6*Y(i+1)-M(i+1)*h(i)2)*X(i)/(6*h(i); end for
5、 i=1 : n-1 Q(i)=M(i)*(X(i+1)-(X(i)+X(i+1)/2)3/(6*h(i)+(M(i+1)*(X(i)+X(i+1)/2-X(i)3)/(6*h(i)+(Y(i) -M(i)*(h(i)2/6)*(X(i+1)-(X(i)+X(i+1)/2)/h(i)+(Y(i+1) -M(i+1)*(h(i)2/6)*(X(i)+X(i+1)/2-X(i)/h(i); end disp(Q) for i=1:n-1 x=X(i):0.001:X(i+1); z=H(i)*x.3+I(i)*x.2+J(i)*x+K(i); plot(x,z,X,Y,*); hold on en
6、d, X=0 1 2 3 4 5 6 7 8 9 10; Y=0.0 0.79 1.53 2.19 2.71 3.03 3.27 2.89 3.06 3.19 3.29; sanciyangtiao8(X,Y,0.8,0.2) 0.3986 1.1684 1.8715 2.4782 2.8733 3.2137 3.0844 2.9199 3.1498 3.2223,function Sanciyangtiao( X, Y ) n = length( X ); for i = 1 : n-1 h(i) = X(i+1)-X(i); end for j = 2 : n-1 u(j) = h(j-1
7、)/( h(j-1) + h(j) ); t(j) = 1 - u(j); d(j) = 6*( (Y(j+1) - Y(j)/h(j) - (Y(j) - Y(j-1)/h(j-1) )/( h(j-1) + h(j) ); end t(1)=0;u(n)=0; d(1) = 0; d(n) = 0; for i = 1 : n A(i,i)=2; A(1,2)=0; A(n,n-1)=0; for j = 2 : n-1 A(j,j-1)=u(j); A(j,j+1)=t(j); if abs(i-j)1 A(i,j) = 0; end end end,D = d; N = AD; M =
8、 N; for i = 1 : n-1 H(i)=(M(i+1)-M(i)/(6*h(i); I(i)=(M(i)*X(i+1)-M(i+1)*X(i)/(2*h(i); J(i)=(M(i+1)*X(i)2-M(i)*X(i+1)2+2*(Y(i+1)-Y(i)+h(i)2/3*(M(i)-M(i+1)/(2*h(i); K(i)=(M(i)*X(i+1)3-M(i+1)*X(i)3+(6*Y(i)-M(i)*h(i)2)*X(i+1)-(6*Y(i+1)-M(i+1)*h(i)2)*X(i)/(6*h(i); end for i=1 : n-1 Q(i)=M(i)*(X(i+1)-(X(i
9、)+X(i+1)/2)3/(6*h(i)+(M(i+1)*(X(i)+X(i+1)/2-X(i)3)/(6*h(i)+(Y(i) -M(i)*(h(i)2/6)*(X(i+1)-(X(i)+X(i+1)/2)/h(i)+(Y(i+1) -M(i+1)*(h(i)2/6)*(X(i)+X(i+1)/2-X(i)/h(i); end disp(Q) for i=1:n-1 x=X(i):0.001:X(i+1); z=H(i)*x.3+I(i)*x.2+J(i)*x+K(i); plot(x,z,X,Y,*); hold on end, X=0 1 2 3 4 5 6 7 8 9 10; Y=0.
10、0 0.79 1.53 2.19 2.71 3.03 3.27 2.89 3.06 3.19 3.29; sanciyangtiao2(X,Y) 0.3984 1.1685 1.8715 2.4782 2.8733 3.2138 3.0841 2.9209 3.1459 3.2368,下面5张是第三题,输入下面命令得拟合图形： fplot(0.5491+(-3.9683e-005)*x+(-2.9977)*x.2+1.9991*x.3,-1.0,2.0) ,输入如下命令得离散数据和拟合曲线的图形： x=-1.0,-0.5,0.0,0.5,1.0,1.5,2.0;y=-4.447,-0.452,0.551,0.048,-0.447,0.549,4.552; X=(-1.0:0.001:2.0);Y=0.5491+(-3.9683e-005)*X+(-2.9977)*X.2+1.9991*X.3; plot(X,Y,-,x,y,*),