功能强大的牛顿插值matlab程序代码

clear;

format long;

way_in = input('请选择输入的内容(1或2):\\n1、输入为f(x)表达式，区间[a,b]及其等分数n的值\\n2、输入为f(x)表达式和插值点横坐标xi的值\\n');

switch way_in

case 1

f = input('请输入函数表达式:f(x) = ', 's');

a = input('请输入区间左端值a：');

b = input('请输入区间右端值b：');

n = input('请输入区间等分值n：');

np = input('请输入插值函数在区间内绘图点数(默认输入100)：');

for i=1:n+1

x(i) = a + (b-a)/n*(i-1);

y(i,1) = eval(subs(f,'x(i)','x'));

end

for j=1:n

for k=j:n

temp=y(k+1,j)-y(k,j);

y(k+1,j+1)=temp/(x(k+1)-x(k+1-j)) ;

end

c(j)=y(j,j);

end

c(j+1)=y(j+1,j+1);

for k=1:np-1

xx(k)= a + (b-a)/np*k;

yy(k) = eval(subs(f,'xx(k)','x'));

end

for k=1:np-1

xs=xx(k);

for i=1:n+1

if i==1

s(i)=c(i);

else

s(i)=c(i);

for j=1:i-1

s(i)=s(i)*(xs-x(j));

end

end

end

Nn(k)=sum(s);

end

way_out = input('请选择要绘出的曲线(1、2或3)：\\n1、同时输出原始曲线f(x)和插值曲线\\n2、只输出插值曲线\\n3、只输出原始曲线\\n');

switch way_out

case 1

figure;

plot(xx,yy,'r');

grid on;

hold on;

plot(xx,Nn,'b');

legend('原始曲线f(x)','插值曲线N(x)');

title('牛顿插值');

case 2

figure;

plot(xx,Nn,'m');

legend('插值曲线N(x)');

title('牛顿插值');

case 3

figure;

plot(xx,yy,'g');

legend('原始曲线f(x)');

title('牛顿插值');

otherwise

errordlg('请正确选择，输入只能为1、2或者3！','提示','on');

end

case 2

f = input('请输入函数表达式:f(x) = ', 's');

xb = input('请输入插值节点的横坐标x:','s');

x = sscanf(xb,'%f');

disp('x0,x1,...,xi分别为：');

disp(x);

n = size(x,1) - 1;

if n<2

errordlg('请至少输入3个xi的值','提示','on');

return;

end

np = input('请输入插值函数在区间内绘图点数(默认输入100)：');

a = x(1);

b = x(n+1);

for i=1:n+1

y(i,1) = eval(subs(f,'x(i)','x'));

end

for j=1:n

for k=j:n

temp=y(k+1,j)- y(k,j);

y(k+1,j+1)=temp/(x(k+1)-x(k+1-j)) ;

end

c(j)=y(j,j);

end

c(j+1)=y(j+1,j+1);

for k=1:np-1

xx(k) = a + (b-a)/np*k;

yy(k) = eval(subs(f,'xx(k)','x'));

end

for k=1:np-1

xs=xx(k);

for i=1:n+1

if i==1

s(i)=c(i);

else

s(i)=c(i);

for j=1:i-1

s(i)=s(i)*(xs-x(j));

end

end

end

Nn(k)=sum(s);

end

way_out = input('请选择要绘出的曲线(1、2或3)：\\n1、同时输出原始曲线f(x)和插值曲线\\n2、只输出插值曲线\\n3、只输出原始曲线\\n');

switch way_out

case 1

figure;

plot(xx,yy,'r');

grid on;

hold on;

plot(xx,Nn,'b');

legend('原始曲线f(x)','插值曲线N(x)');

title('牛顿插值');

case 2

figure;

plot(xx,Nn,'m');

legend('插值曲线N(x)');

title('牛顿插值');

case 3

figure;

plot(xx,yy,'g');

legend('原始曲线f(x)');

title('牛顿插值');

otherwise

errordlg('请正确选择，输入只能为1、2或者3！','提示','on');

end

otherwise

errordlg('请正确选择，输入只能为1或2！','提示','on');

end