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1111.201)()20)...(2)(1()(kkxxxxxpE1-1l220200)(19xxp(E1-2)E1-119xE1-1E1-2E1-1Matlabrootspolyurootsaa1nuna121,...,,naaau0...1121nnnnaxaxaxab=poly(v)bn1nvrootsPoly.ve=zeros(1,21);ve(2)=ess;roots(poly(1:20))+ve)MatlabE1-2essE1-21essE1-1(E1-2)2E1-218x21functiont_charpt1_1clcresult=inputdlg({':[020]:'},'charpt1_1',1,{'19'});Numb=str2num(char(result));if((Numb20)|(Numb0))errordlg(':[020]!');return;endresult=inputdlg({'(01):'},'charpt1_1',1,{'0.00001'});ess=str2num(char(result));ve=zeros(1,21);ve(21-Numb)=ess;root=roots(poly(1:20)+ve);x0=real(root);y0=imag(root);plot(x0',y0','*');disp(['',num2str(Numb),'',num2str(ess),':']);disp(num2str(root));ess1e-6,1e-8.1e-10,1e-12.191e-006:21.3025+1.56717i21.3025-1.56717i18.5028+3.6004i18.5028-3.6004i15.1651+3.76125i15.1651-3.76125i12.4866+2.88278i12.4866-2.88278i10.5225+1.71959i10.5225-1.71959i9.04485+0.594589i9.04485-0.594589i7.9489+0i7.00247+0i5.99995+0i5+0i4+0i3+0i2+0i1+0i191e-010:19.9953+0i19.0323+0i17.8696+0i17.2186+0i15.4988+0.0211828i15.4988-0.0211828i13.7707+0i13.1598+0i11.9343+0i11.029+0i9.99073+0i9.00247+0i7.99952+0i7.00007+0i5.99999+0i5+0i4+0i3+0i2+0i1+0iess1e-6,1e-8.1e-10,1e-123essE.1.1E.1.2ess2x18ess=1e-009ess=1e-008x19(ess=1e-009)x18x19x8ess=1000xess=10e10xnn22Runge)(xLn]1,1[22511)(xxf]1,1[ninixi,...,2,1,0,21niiinxlxxL02)(2511)()(xlini,...,2,1,0nl,...3,2n)(xf)(xLn]1,1[2[-55]4xxgxxxharctan)(,1)(43],[ba1,...,2,1,)1(2()12(cos22nknkababxk121,...,,nxxx1functiony=Lagrange(x0,y0,x);%Lagrangen=length(x0);m=length(x);fori=1:mz=x(i);s=0.0;fork=1:np=1.0;forj=1:nif(j~=k)p=p*(z-x0(j))/(x0(k)-x0(j));endends=s+p*y0(k);endy(i)=s;endfunctiont_charpt2promps={'f(x),f,h(x),h,g(x),g:'};titles='charpt_2';result=inputdlg(promps,'charpt2',1,{'f'});Nb_f=char(result);if(Nb_f~='f'&Nb_f~='h'&Nb_f~='g')errordlg('');return;endresult=inputdlg({'N:'},'charpt_2',1,{'10'});Nd=str2num(char(result));if(Nd1)errordlg('');return;endswitchNb_f5case'f'f=inline('1./(1+25*x.^2)');a=-1;b=1;case'h'f=inline('x./(1+x.^4)');a=-5;b=5;case'g'f=inline('atan(x)');a=-5;b=5;endx0=linspace(a,b,Nd+1);y0=feval(f,x0);x=a:0.1:b;y=Lagrange(x0,y0,x);fplot(f,[ab],'co');holdon;plot(x,y,'b--');xlabel('x');ylabel('y=f(x)oandy=Ln(x)--');n=23n=3n=6n=7n=8nx=0f(x)x=-1x=1nn2f(x)h(x)g(x)h(x),g(x)[-55]h(x)=x/(1+x4)g(x)=arctanx6h(x),n=7h(x),n=8h(x),n=9h(x),n=10g(x),n=8g(x),n=9g(x),n=12g(x),n=13nx=0f(x)x=-5x=5nnf(x)h(x)g(x)nLagrangeLn(x)xn-1h(x)g(x)nLagrangeLn(x)xn-1h(x)g(x)7332.MatabsplineMatlabsplineB-12kx012345678910ky0.00.791.532.192.713.033.272.893.063.193.29'ky0.80.21functiont_charpt2promps={'f(x),f,h(x),h,g(x),g:'};titles='charpt_2';result=inputdlg(promps,'charpt2',1,{'f'});Nb_f=char(result);if(Nb_f~='f'&Nb_f~='h'&Nb_f~='g')errordlg('');return;endresult=inputdlg({'N:'},'charpt_2',1,{'10'});Nd=str2num(char(result));if(Nd1)errordlg('');return;endswitchNb_fcase'f'f=inline('1./(1+25*x.^2)');a=-1;b=1;case'h'f=inline('x./(1+x.^4)');a=-5;b=5;case'g'8f=inline('atan(x)');a=-5;b=5;endx0=linspace(a,b,Nd+1);y0=feval(f,x0);x=a:0.1:b;cs=spline(x0,y0);y=ppval(cs,x);plot(x0,y0,'o');holdon;plot(x,y,'k-');xlabel('x');ylabel('y=f(x)oandy=Spline(x)-');f(x),n=5n=10n=20h(x),n=5h(x),n=10n=20g(x),n=5n=10n=202x0=0:10;y0=[0.00.791.532.192.713.033.272.893.063.193.29];x=0:0.1:10;pp=csape(x0,y0,'complete',[0.80.2]);y=ppval(pp,x);plot(x0,y0,'o');holdon;plot(x,y,'k-');xlabel('x');ylabel('y=f(x)oandy=Spline(x)-');9