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1、第4章习题参考答案1.有如下数据:X11.11.21.31.4y1.000001.233681.552711.993722.61170利用本章介绍的几种插值方法对其进行插值,得到每隔0.05的结果。编写脚本文件,文件内容为:%Interpolationusingthefourmethodsx=[11.11.21.31.4];y=[1.000001.233681.552711.993722.61170];length_of_x=length(x);scalar_x=x(1):0.05:x(length_of_x);
2、length_of_sx=length(scalar_x);y_nearest=zeros(length(scalar_x),1);y_linear=zeros(length(scalar_x),1);y_spline=zeros(length(scalar_x),1);y_cubic=zeros(length(scalar_x),1);fori=1:length_of_sxy_nearest(i)=interp1(x,y,scalar_x(i),'nearest');y_linear(i)=interp1(x,
3、y,scalar_x(i),'linear');y_spline(i)=interp1(x,y,scalar_x(i),'spline');y_cubic(i)=interp1(x,y,scalar_x(i),'cubic');endsubplot(2,2,1),plot(x,y,'*'),holdon,plot(scalar_x,y_nearest),title('method=nearest');subplot(2,2,2),plot(x,y,'*'),holdon,plot(scalar_x,y_linea
4、r),title('method=linear');subplot(2,2,3),plot(x,y,'*'),holdon,plot(scalar_x,y_spline),title('method=spline');subplot(2,2,4),plot(x,y,'*'),holdon,plot(scalar_x,y_cubic),title('method=cubic');得到结果为:2.求函数,初始点为的解,并绘制图形。参考答案:>>y=@(x)exp(x)-x^5;>>x=fzero(y,8)x=12.7
5、132>>fplot(y,[x-1,x+1]);>>holdon>>plot(x,y(x),'r*');3.求下列函数的极值。(1)(2)参考答案:(1)>>z=@(x)x(1)^2-(x(2)-1)^2;>>[x,fvalue,flag,output]=fminsearch(z,[0,0])Exiting:Maximumnumberoffunctionevaluationshasbeenexceeded-increaseMaxFunEvalsoption.Currentfunctionvalue:-359212
6、266339440800000000000000000000000000000000000000000000000000000000000000000000.000000x=1.0e+41*0.9523-6.0686fvalue=-3.5921e+83flag=0output=iterations:200funcCount:401algorithm:'Nelder-Meadsimplexdirectsearch'message:[1x233char](2)>>z=@(x)(x(1)-x(2)+1)^2;>>[x,
7、fvalue,flag,output]=fminsearch(z,[0,0])x=-0.54250.4575fvalue=2.4109e-11flag=1output=iterations:40funcCount:74algorithm:'Nelder-Meadsimplexdirectsearch'message:[1x194char]4.计算下列积分。(1)(2)参考答案:(1)>>f=@(x)x+x.^3+x.^5;>>q=quad(f,-1,1)q=2.2204e-16(2)>>f5=@(x,y)sin(
8、y).*(x+y)./(x.^2+4);>>q=dblquad(f5,1,10,1,10)q=5.5254