Matlab实现——Differentiation Using Limits

difflim.m

%Program 6.1 (Differentiation Using Limits). To approximate 
%f'(x) numerically by generating the sequencef'(x)≈Dk=
%[f(x+(10^-k)*h)-f(x-(10^-k)*h]/[2*(10-k)*h]  for k=0,… ,n
%until |Dn+1-Dn| > |Dn-Dn-1| or |Dn-Dn-1| < tolerance, 
%which is an attempt to find the best approximation f’(x)≈Dn.
function  [L,n]=difflim(f,x,toler)
%Input  - f is the function input as a string 'f '
%       - x is the differentiation point
%       - toler is the desired tolerance
%Output - L=[H' D' E']: 
%                    H is the vector of step sizes
%                    D is the vector of approximate derivatives
%                    E is the vector of error bounds
%         - n is the coordinate of the "best approximation"
max1=15;
h=1;
H(1)=h;
D(1)=(feval(f,x+h)-feval(f,x-h))/(2*h);
E(1)=0;
R(1)=0;
for n=1:2
   h=h/10;
   H(n+1)=h;
   D(n+1)=(feval(f,x+h)-feval(f,x-h))/(2*h);
   E(n+1)=abs(D(n+1)-D(n));
   R(n+1)=2*E(n+1)/(abs(D(n+1))+abs(D(n))+eps);
end
n=2;
while((E(n)>E(n+1))&(R(n)>toler))&n<max1
   h=h/10;
   H(n+2)=h;
   D(n+2)=(feval(f,x+h)-feval(f,x-h))/(2*h);
   E(n+2)=abs(D(n+2)-D(n+1));
   R(n+2)=2*E(n+2)/(abs(D(n+2))+abs(D(n+1))+eps);
   n=n+1;
end
n=length(D)-1;
L=[H' D' E'];%Program 6.1 (Differentiation Us