數(shù)值分析第五版計(jì)算實(shí)習(xí)題

1、數(shù)值分析計(jì)算實(shí)習(xí)題數(shù)值分析計(jì)算實(shí)習(xí)題第二章21程序：clearclcx1=[0.20.40.60.81.0]y1=[0.980.920.810.640.38]n=length(y1)c=y1(:)fj=2:n%求差商fi=n:1:jc(i)=(c(i)c(i1))(x1(i)x1(ij1))endendsymsxdfddf(1)=1d(1)=y1(1)fi=2:n%求牛頓差值多項(xiàng)式df(i)=df(i1)(xx1(i1))d(i)=c(

2、i)df(i)enddisp(4次牛頓插值多項(xiàng)式)P4=vpa(collect((sum(d)))5)%P4即為4次牛頓插值多項(xiàng)式并保留小數(shù)點(diǎn)后5位數(shù)pp=csape(x1y1variational)%調(diào)用三次樣條函數(shù)q=pp.coefsdisp(三次樣條函數(shù))fi=1:4S=q(i:)[(xx1(i))^3(xx1(i))^2(xx1(i))1]S=vpa(collect(S)5)endx2=0.2:0.08:1.08dot=[121

3、112]figureezplot(P4[0.21.08])holdony2=fnval(ppx2)x=x2(dot)y3=eval(P4)y4=fnval(ppx2(dot))plot(x2y2rx2(dot)y3bx2(dot)y4co)title(4次牛頓插值及三次樣條)結(jié)果如下：4次牛頓插值多項(xiàng)式P4=0.52083x^40.83333x^31.1042x^20.19167x0.98三次樣條函數(shù)Dw=zeros(1n)fi=1:n

4、Dw(i)=y1(i)polyval(q(i:)x1(i))%系數(shù)endp=DwqsymsxL8fi=1:nL8(i)=p(ni1)x^(i1)enddisp(8次拉格朗日插值)L8=vpa(collect((sum(L8)))5)xi=0:64yi=polyval(pxi)figureplot(xiyix1y1r)holdontitle(8次拉格朗日插值)結(jié)果如下：8次拉格朗日插值L8=3.2806e10x^86.7127e8x^75