i2 = 3; end for j=1:3
j1 = mod(j+1,3); if(j1 == 0) j1 = 3; end
j2 = mod(j+2,3); if(j2 == 0) j2 = 3; end
f = f+Z(cx(i),cy(j))*((t-x(cx(i1)))*(t-x(cx(i2)))/(x(cx(i))-x(cx(i1)))/(x(cx(i))-x(cx(i2))))* ... (s-y(cy(j1)))*(s-y(cy(j2)))/(y(cy(j))-y(cy(j1)))/(y(cy(j))-y(cy(j2))); %插值多项式 end end
fz = subs(f,'[t s]',[x0 y0]);
7.FCZ
function fz = DTL(x,y,Z,x0,y0) syms s t; f = 0.0;
n = length(x); m = length(y);
for i=1:n
if(x(i)<=x0)&& (x(i+1)>=x0) index_x = i; break; end
end %找到x0所在区间 for i=1:m
if(y(i)<=y0)&& (y(i+1)>=y0) index_y = i; break; end
end %找到y0所在区间
if index_x == 1
cx(1:3) = index_x:(index_x+2); else
if index_x == n-1
cx(1:3) = (index_x-1):(index_x+1); else
if abs(x(index_x-1)-x0)>abs(x(index_x+2)-x0) cx(1:3) = (index_x):(index_x+2); else
cx(1:3) = (index_x-1):(index_x+1); end end
end %找到离x0最近的三个x坐标
if index_y == 1
cy(1:3) = index_y:(index_y+2); else
if index_y == m-1
cy(1:3) = (index_y-1):(index_y+1); else
if abs(y(index_y-1)-y0)>=abs(y(index_y+2)-y0) cy(1:3) = (index_y):(index_y+2); else
cy(1:3) = (index_y-1):(index_y+1); end end
end %找到离y0最近的三个y坐标
for i=1:3 i1 = mod(i+1,3); if(i1 == 0) i1 = 3; end
i2 = mod(i+2,3); if(i2 == 0) i2 = 3; end for j=1:3
j1 = mod(j+1,3); if(j1 == 0) j1 = 3; end
j2 = mod(j+2,3); if(j2 == 0) j2 = 3; end
f = f+Z(cx(i),cy(j))*((t-x(cx(i1)))*(t-x(cx(i2)))/(x(cx(i))-x(cx(i1)))/(x(cx(i))-x(cx(i2))))* ... (s-y(cy(j1)))*(s-y(cy(j2)))/(y(cy(j))-y(cy(j1)))/(y(cy(j))-y(cy(j2))); %插值多项式 end
end
fz = subs(f,'[t s]',[x0 y0]);
8.Gauss
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
9.Hermite
function f = Hermite(x,y,y_1,x0) syms t; f = 0.0;
if(length(x) == length(y))
if(length(y) == length(y_1)) n = length(x);