MATLAB实现插值算法，案例丰富【数学建模、科学计算算法】.zip

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