function f = Gauss(x,y,x0)
if(length(x) == length(y))
n = length(x);
else
disp('x和y的维数不相等!');
return;
end
xx =linspace(x(1),x(n),(x(2)-x(1)));
if(xx ~= x)
disp('节点之间不是等距的!');
return;
end
if( mod(n,2) ==1)
if(nargin == 2)
f = GStirling(x,y,n);
else if(nargin == 3)
f = GStirling(x,y,n,x0);
end
end
else
if(nargin == 2)
f = GBessel(x,y,n);
else if(nargin == 3)
f = GBessel(x,y,n,x0);
end
end
end
function f = GStirling(x,y,n,x0)
syms t;
nn = (n+1)/2;
f = y(nn);
for(i=1:n-1)
for(j=i+1:n)
y1(j) = y(j)-y(j-1);
end
if(mod(i,2)==1)
c(i) = (y1((i+n)/2)+y1((i+n+2)/2))/2;
else
c(i) = y1((i+n+1)/2)/2;
end
if(mod(i,2)==1)
l = t+(i-1)/2;
for(k=1:i-1)
l = l*(t+(i-1)/2-k);
end
else
l_1 = t+i/2-1;
l_2 = t+i/2;
for(k=1:i-1)
l_1 = l_1*(t+i/2-1-k);
l_2 = l_2*(t+i/2-k);
end
l = l_1 + l_2;
end
l = l/factorial(i);
f = f + c(i)*l;
simplify(f);
f = vpa(f, 6);
y = y1;
if(i==n-1)
if(nargin == 4)
f = subs(f,'t',(x0-x(nn))/(x(2)-x(1)));
end
end
end
function f = GBessel(x,y,n,x0)
syms t;
nn = n/2;
f = (y(nn)+y(nn+1))/2;
for(i=1:n-1)
for(j=i+1:n)
y1(j) = y(j)-y(j-1);
end
if(mod(i,2)==1)
c(i) = y1((i+n+1)/2)/2;
else
c(i) = (y1((i+n)/2)+y1((i+n+2)/2))/2;
end
if(mod(i,2)==0)
l = t+i/2-1;
for(k=1:i-1)
l = l*(t+i/2-1-k);
end
else
l_1 = t+(i-1)/2;
l_2 = t+(i-1)/2-1;
for(k=1:i-1)
l_1 = l_1*(t+(i-1)/2-k);
l_2 = l_2*(t+(i-1)/2-1-k);
end
l = l_1 + l_2;
end
l = l/factorial(i);
f = f + c(i)*l;
simplify(f);
f = vpa(f, 6);
y = y1;
if(i==n-1)
if(nargin == 4)
f = subs(f,'t',(x0-x(nn))/(x(2)-x(1)));
end
end
end