Romberg code isn't running correctly.

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Michael Sipes
Michael Sipes 2015-12-1
评论： Are Mjaavatten 2016-1-12
I am trying to write code for Romberg integration and am getting a error message when I run the program. Can someone help me with the problem please. Thanks
function Rnum = MSipesR(f,a,b,m)
% Integration algorithm based on Romberg extrapolation
% f - string input for function y = f(x) (e.g. f = 'x.^6')
% a - lower limit of integration
% b - upper limit of integration
% m - maximal number of Romberg iterations
% Rnum - row-vector of numerical approximations for the integral of f(x) between x = a and x = b:
% the entry with index k in Rnum corresponds to the approximation of order O(h^(2k))
R = ones(m,m); % the matrix for Romberg approximations
hmin = (b-a)/2^(m-1); % the minimal step size
for k = 1 : m
h = 2^(k-1)*hmin; % the step size for the k-th row of the Romberg matrix
x = a : h : b;
f1 = eval(f);
k1 = length(f1);
R(k,1) = 0.5*h*(f1(1) + 2*sum(f1(2:k1-1)) + f1(k1)); % trapezoidal rule for the first column of the Romberg matrix
end
for k = 2 : m % compute the k-th column of the Romberg matrix
for kk = 1 : (m-k+1) % the matrix of Romberg approximations is triangular!
R(kk,k) = R(kk,k-1)+(R(kk,k-1) - R(kk+1,k-1))/(4^(k-1)-1); % see the Romberg integration algorithm
end
end
% define the vector Rnum for numerical approximations
Rnum = R(1,:);
  1 个评论
Are Mjaavatten
Are Mjaavatten 2016-1-12
What is the problem? It seems to work very nicely for me:
Rnum = MSipesR('x.^6',0,1,4)
Rnum =
0.1506 0.1430 0.1429 0.1429
Check, using quad:
quad(@(x) x.^6,0,1)
ans =
0.1429

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