h0=figure('toolbar','none',...
    'position',[200 50 350 450],...
    'name','實(shí)例85');
h1=axes('parent',h0,...
    'position',[0.10 0.45 0.8 0.5],...
    'visible','off');
x=0:0.2:2*pi;
y=sin(x);
plot(x,y)
b1=uicontrol('parent',h0,...
    'units','points',...
    'tag','b1',...
    'style','pushbutton',...
    'string','拉格朗日插值',...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[20 60 70 20],...
    'callback',[...
        'cla,',...
        'strn=get(e1,''string'');,',...
        'n=str2num(strn);,',...
        'i=1;,',...
        'x=0:0.2:2*pi;,',...
        'for t=0:0.2:2*pi,',...
        'y(i)=sin(t);,',...
        'L(i)=lag(t,n);,',...
        'i=i+1;,',...
        'end,',...
        'plot(x,y,''b*'',x,L,''r-''),',...
        'legend(''sin(x)'',''插值函數(shù)'');,',...
        'axis([0 7 -1.5 1.5])']);
b2=uicontrol('parent',h0,...
    'units','points',...
    'tag','b2',...
    'style','pushbutton',...
    'string','誤差比較',...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[170 60 70 20],...
    'callback',[...
        'strn=get(e1,''string'');,',...
        'n=str2num(strn);,',...
        'strm=get(e2,''string'');,',...
        'm=str2num(strm);,',...
        'dd=abs(sin(m)-lag(m,n));,',...
        'msgbox([''誤差為：'',num2str(dd)],''計(jì)算結(jié)果'')']);
e1=uicontrol('parent',h0,...
    'units','points',...
    'tag','e1',...
    'style','edit',...
    'fontsize',12,...
    'string','5',...
    'horizontalalignment','right',...
    'backgroundcolor',[1 1 1],...
    'position',[50 100 40 20]);
e2=uicontrol('parent',h0,...
    'units','points',...
    'tag','e2',...
    'style','edit',...
    'fontsize',12,...
    'string','1.20',...
    'horizontalalignment','right',...
    'backgroundcolor',[1 1 1],...
    'position',[200 100 40 20]);
t1=uicontrol('parent',h0,...
    'units','points',...
    'tag','t1',...
    'style','text',...
    'string','階數(shù)：',...
    'fontsize',12,...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[20 100 30 20]);
t2=uicontrol('parent',h0,...
    'units','points',...
    'tag','t2',...
    'style','text',...
    'string','誤差點(diǎn)：',...
    'fontsize',12,...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[160 100 40 20]);
b3=uicontrol('parent',h0,...
    'units','points',...
    'tag','b3',...
    'style','pushbutton',...
    'string','關(guān)閉',...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[100 20 60 20],...
    'callback','close');

例86：三次樣條插值法

h0=figure('toolbar','none',...
    'position',[200 50 350 450],...
    'name','實(shí)例86');
h1=axes('parent',h0,...
    'position',[0.10 0.45 0.8 0.5],...
    'visible','off');
x=0:0.2:2*pi;
y=sin(x);
plot(x,y)
b1=uicontrol('parent',h0,...
    'units','points',...
    'tag','b1',...
    'style','pushbutton',...
    'string','三次樣條插值',...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[20 60 70 20],...
    'callback',[...
        'y=0,',...
        'sy=0,',...
        'strn1=get(e2,''string'');,',...
        'n1=str2num(strn1);,',...
        'strn2=get(e3,''string'');,',...
        'n2=str2num(strn2);,',...
        'x=n1:0.2:n2;,',...
        'i=1;,',...
        'for t=n1:0.2:n2,',...
        'y(i)=sin(t);,',...
        'sy(i)=san(t,n1,n2);,',...
        'i=i+1;,',...
        'end,',...
        'plot(x,y,''b*'',x,sy,''r-''),',...
        'axis([0 7 -1.5 1.5]),',...
        'legend(''sin(x)'',''N-Hermite插值'')']);
b2=uicontrol('parent',h0,...
    'units','points',...
    'tag','b2',...
    'style','pushbutton',...
    'string','誤差比較',...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[170 60 70 20],...
    'callback',[...
        'strdn1=get(e2,''string'');,',...
        'n1=str2num(strdn1);,',...
        'strdn2=get(e3,''string'');,',...
        'n2=str2num(strdn2);,',...
        'strdn=get(e1,''string'');,',...
        'dn=str2num(strdn);,',...
        'dd=abs(sin(dn)-san(dn,n1,n2));,',...
        'msgbox([''誤差為：'',num2str(dd)],''計(jì)算結(jié)果'')']);
e1=uicontrol('parent',h0,...
    'units','points',...
    'tag','e1',...
    'style','edit',...
    'fontsize',12,...
    'string','1.20',...
    'horizontalalignment','right',...
    'backgroundcolor',[1 1 1],...
    'position',[200 100 40 20]);
t1=uicontrol('parent',h0,...
    'units','points',...
    'tag','t1',...
    'style','text',...
    'string','誤差點(diǎn)：',...
    'fontsize',12,...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[160 100 40 20]);
e2=uicontrol('parent',h0,...
    'units','points',...
    'tag','e2',...
    'style','edit',...
    'fontsize',12,...
    'string','1.00',...
    'horizontalalignment','right',...
    'backgroundcolor',[1 1 1],...
    'position',[20 85 40 20]);
t2=uicontrol('parent',h0,...
    'units','points',...
    'tag','t2',...
    'style','text',...
    'string','第一節(jié)點(diǎn)：',...
    'fontsize',12,...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[15 105 50 20]);
e3=uicontrol('parent',h0,...
    'units','points',...
    'tag','e3',...
    'style','edit',...
    'fontsize',12,...
    'string','3.00',...
    'horizontalalignment','right',...
    'backgroundcolor',[1 1 1],...
    'position',[100 85 40 20]);
t3=uicontrol('parent',h0,...
    'units','points',...
    'tag','t3',...
    'style','text',...
    'string','第二節(jié)點(diǎn)：',...
    'fontsize',12,...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[95 105 50 20]);
b3=uicontrol('parent',h0,...
    'units','points',...
    'tag','b3',...
    'style','pushbutton',...
    'string','關(guān)閉',...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[100 20 60 20],...
    'callback','close');

實(shí)例87：NEWTON插值

h0=figure('toolbar','none',...
    'position',[200 50 350 450],...
    'name','實(shí)例87');
h1=axes('parent',h0,...
    'position',[0.10 0.45 0.8 0.5],...
    'visible','off');
x=0:0.2:2*pi;
y=sin(x);
plot(x,y)
b1=uicontrol('parent',h0,...
    'units','points',...
    'tag','b1',...
    'style','pushbutton',...
    'string','牛頓插值',...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[20 60 70 20],...
    'callback',[...
        'strn=get(e1,''string'');,',...
        'n=str2num(strn);,',...
        'x=0:0.2:2*pi;,',...
        'i=1;,',...
        'for t=0:0.2:2*pi,',...
        'y(i)=sin(t);,',...
        'ynt(i)=newton(t,n);,',...
        'i=i+1;,',...
        'end,',...
        'plot(x,y,''b*'',x,ynt,''r-''),',...
        'axis([0 7 -1.5 1.5]),',...
        'legend(''sin(x)'',''牛頓插值'')']);
b2=uicontrol('parent',h0,...
    'units','points',...
    'tag','b2',...
    'style','pushbutton',...
    'string','誤差比較',...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[170 60 70 20],...
    'callback',[...
        'strn=get(e1,''string'');,',...
        'n=str2num(strn);,',...
        'strdn=get(e2,''string'');,',...
        'dn=str2num(strdn);,',...
        'dd=abs(sin(dn)-newton(dn,n));,',...
        'msgbox([''誤差為：'',num2str(dd)],''計(jì)算結(jié)果'')']);
e1=uicontrol('parent',h0,...
    'units','points',...
    'tag','e1',...
    'style','edit',...
    'fontsize',12,...
    'string','5',...
    'horizontalalignment','right',...
    'backgroundcolor',[1 1 1],...
    'position',[50 100 40 20]);
e2=uicontrol('parent',h0,...
    'units','points',...
    'tag','e2',...
    'style','edit',...
    'fontsize',12,...
    'string','1.20',...
    'horizontalalignment','right',...
    'backgroundcolor',[1 1 1],...
    'position',[200 100 40 20]);
t1=uicontrol('parent',h0,...
    'units','points',...
    'tag','t1',...
    'style','text',...
    'string','節(jié)點(diǎn)數(shù)：（<6）',...
    'fontsize',12,...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[10 100 40 30]);
t2=uicontrol('parent',h0,...
    'units','points',...
    'tag','t2',...
    'style','text',...
    'string','誤差點(diǎn)：',...
    'fontsize',12,...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[160 100 40 20]);
b3=uicontrol('parent',h0,...
    'units','points',...
    'tag','b3',...
    'style','pushbutton',...
    'string','關(guān)閉',...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[100 20 60 20],...
    'callback','close');

實(shí)例88：hermite插值

h0=figure('toolbar','none',...
    'position',[200 50 350 450],...
    'name','實(shí)例88');
h1=axes('parent',h0,...
    'position',[0.10 0.45 0.8 0.5],...
    'visible','off');
x=0:0.2:2*pi;
y=sin(x);
plot(x,y)
b1=uicontrol('parent',h0,...
    'units','points',...
    'tag','b1',...
    'style','pushbutton',...
    'string','Hermite插值',...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[20 60 70 20],...
    'callback',[...
        'strn1=get(e2,''string'');,',...
        'n1=str2num(strn1);,',...
        'strn2=get(e3,''string'');,',...
        'n2=str2num(strn2);,',...
        'x=0:0.2:2*pi;,',...
        'i=1;,',...
        'for t=0:0.2:2*pi,',...
        'y(i)=sin(t);,',...
        'ynt(i)=hermite(t,n1,n2);,',...
        'i=i+1;,',...
        'end,',...
        'plot(x,y,''b*'',x,ynt,''r-''),',...
        'axis([0 7 -1.5 1.5]),',...
        'legend(''sin(x)'',''Hermite插值'')']);
b2=uicontrol('parent',h0,...
    'units','points',...
    'tag','b2',...
    'style','pushbutton',...
    'string','誤差比較',...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[170 60 70 20],...
    'callback',[...
        'strn1=get(e2,''string'');,',...
        'n1=str2num(strn1);,',...
        'strn2=get(e3,''string'');,',...
        'n2=str2num(strn2);,',...
        'dn=str2num(strdn);,',...
        'dd=abs(sin(dn)-hermite(dn,n1,n2));,',...
        'msgbox([''誤差為：'',num2str(dd)],''計(jì)算結(jié)果'')']);
e1=uicontrol('parent',h0,...
    'units','points',...
    'tag','e1',...
    'style','edit',...
    'fontsize',12,...
    'string','1.20',...
    'horizontalalignment','right',...
    'backgroundcolor',[1 1 1],...
    'position',[200 100 40 20]);
t1=uicontrol('parent',h0,...
    'units','points',...
    'tag','t1',...
    'style','text',...
    'string','誤差點(diǎn)：',...
    'fontsize',12,...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[160 100 40 20]);
e2=uicontrol('parent',h0,...
    'units','points',...
    'tag','e2',...
    'style','edit',...
    'fontsize',12,...
    'string','1.00',...
    'horizontalalignment','right',...
    'backgroundcolor',[1 1 1],...
    'position',[20 85 40 20]);
t2=uicontrol('parent',h0,...
    'units','points',...
    'tag','t2',...
    'style','text',...
    'string','第一節(jié)點(diǎn)：',...
    'fontsize',12,...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[15 105 50 20]);
e3=uicontrol('parent',h0,...
    'units','points',...
    'tag','e3',...
    'style','edit',...
    'fontsize',12,...
    'string','3.00',...
    'horizontalalignment','right',...
    'backgroundcolor',[1 1 1],...
    'position',[100 85 40 20]);
t3=uicontrol('parent',h0,...
    'units','points',...
    'tag','t3',...
    'style','text',...
    'string','第二節(jié)點(diǎn)：',...
    'fontsize',12,...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[95 105 50 20]);
b3=uicontrol('parent',h0,...
    'units','points',...
    'tag','b3',...
    'style','pushbutton',...
    'string','關(guān)閉',...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[100 20 60 20],...
    'callback','close');

實(shí)例89：mewton形式的hermite插值

h0=figure('toolbar','none',...
    'position',[200 50 350 450],...
    'name','實(shí)例89');
h1=axes('parent',h0,...
    'position',[0.10 0.45 0.8 0.5],...
    'visible','off');
x=0:0.2:2*pi;
y=sin(x);
plot(x,y)
b1=uicontrol('parent',h0,...
    'units','points',...
    'tag','b1',...
    'style','pushbutton',...
    'string','N-Hermite插值',...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[20 60 70 20],...
    'callback',[...
        'strn1=get(e2,''string'');,',...
        'n1=str2num(strn1);,',...
        'strn2=get(e3,''string'');,',...
        'n2=str2num(strn2);,',...
        'x=0:0.2:2*pi;,',...
        'i=1;,',...
        'for t=0:0.2:2*pi,',...
        'y(i)=sin(t);,',...
        'ynh(i)=nhermite(t,n1,n2);,',...
        'i=i+1;,',...
        'end,',...
        'plot(x,y,''b*'',x,ynh,''r-''),',...
        'axis([0 7 -1.5 1.5]),',...
        'legend(''sin(x)'',''N-Hermite插值'')']);
b2=uicontrol('parent',h0,...
    'units','points',...
    'tag','b2',...
    'style','pushbutton',...
    'string','誤差比較',...
    'backgroundcolor',[0.75 0.75 0.75],...
    'position',[170 60 70 20],...
    'callback',[...
        'strdn1=get(e2,''string'');,',...
        'n1=str2num(strdn1);,',...
        'strdn2=get(e3,''string'');,',...