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1、第三章习题及参考答案解答：>>p=[1-1-1];>>roots(p)ans=-0.61801.6180解答：取n=5，m=61>>x=linspace(0,2*pi,5);y=sin(x);>>xi=linspace(0,2*pi,61);>>y0=sin(xi);>>y1=interp1(x,y,xi);>>y2=interp1(x,y,xi,'spline');>>plot(xi,y0,'o',xi,y1,xi,y2,'-.');>>subplot(2,1,1);plot(xi,y1-y0);gridon>>sub
2、plot(2,1,2);plot(xi,y2-y0);gridon分段线性和三次样条插值方法与精确值之差取n=11，m=61>>x=linspace(0,2*pi,11);y=sin(x);>>xi=linspace(0,2*pi,61);>>y0=sin(xi);>>y1=interp1(x,y,xi);>>y2=interp1(x,y,xi,'spline');>>plot(xi,y0,'o',xi,y1,xi,y2,'-.');>>subplot(2,1,1);plot(xi,y1-y0);gridon>>subp
3、lot(2,1,2);plot(xi,y2-y0);gridon分段线性和三次样条插值方法与精确值之差解答：>>x=[0,300,600,1000,1500,2000];>>y=[0.9689,0.9322,0.8969,0.8519,0.7989,0.7491];>>xi=0:100:2000;>>y0=1.0332*exp(-(xi+500)/7756);>>y1=interp1(x,y,xi,'spline');>>p3=polyfit(x,y,3);>>y3=polyval(p3,xi);>>subplot(2,
4、1,1);plot(xi,y0,'o',xi,y1,xi,y3,'-.');>>subplot(2,1,2);plot(xi,y1-y0,xi,y3-y0);gridon插值和拟合方法相比较，都合理，误差也相近。解答：梯形法积分>>x=-3:0.01:3;>>y=exp(-x.^2/2);>>z=trapz(x,y)/(2*pi)z=0.3979辛普森积分>>z=quad('exp(-x.^2/2)',-3,3)/(2*pi)z=0.3979积分区间改为-5~5：梯形法积分>>x=-5:0.01:5;>>y=exp(-x
5、.^2/2);>>z=trapz(x,y)/(2*pi)z=0.3989辛普森积分>>z=quad('exp(-x.^2/2)',-5,5)/(2*pi)z=0.3989积分区间改变了，两种积分的结果依然相同。梯形积分中改变x的维数为2维数组>>x(1,:)=-5:0.01:5>>x(2,:)=-5:0.01:5>>y=exp(-x.^2/2);>>z=trapz(x,y)/(2*pi)???Errorusing==>trapzLENGTH(X)mustequalthelengthofthefirstnon-single
6、tondimensionofY.结论参考教材第82页。解答：>>x=linspace(0,1,4);>>y=x./(x.^2+4);>>t=cumsum(y)*(1-0)/(4-1);>>z1=t(end)>>z2=trapz(x,y)>>z3=quad('x./(x.^2+4)',0,1)>>z4=quadl('x./(x.^2+4)',0,1)z1=0.1437z2=0.1104z3=0.1116z4=0.1116解答：>>A=[5121;2511;12102;12210];>>b=[991515]';>>tol=1
7、.0*10^-6;>>imax=5;>>x0=zeros(1,4);>>tx=jacobi(A,b,imax,x0,tol);>>forj=1:size(tx,1)fprintf('%4d%4.2f%4.2f%4.2f%4.2f',...j-1,tx(j,1),tx(j,2),tx(j,3),tx(j,4))end00.000.000.000.0011.801.801.501.5020.540.480.660.6631.311.321.221.2240.810.790.860.8651.131.131.091.090
8、0.000.000.000.0011.801.081.100.8820.971.021.021.0030.991.001.001.0041.001.001.001.0051.001.001.001.00解答：>>A=[5121;2511;12102;12210];>>b=[991515]';>>tol=1.0*10^
