ALTSUM

Convergence acceleration of alternating series.

Description

Estimates the sum of an alternating series. Three linear methods for convergence acceleration are implemented.

EXAMPLES:

% log(2) = 1 - 1/2 + 1/3 - 1/4 + ...
altsum(1./(1:20))
ans =
   0.693147180559945
 
% pi = 4 - 4/3 + 4/5 - 4/7 + ...
altsum(4./(1:2:39))
ans =
   3.141592653589794
 
% Euler-Mascheroni constant
k = 2:20;
altsum(log(k)./k)/log(2) + log(2)/2
ans =
   0.577215664901533
 
% Divergent series
altsum(1:9,'euler')
ans =
   0.250000000000000

For a review of several acceleration methods see
http://numbers.computation.free.fr/Constants/Miscellaneous/seriesacceleration.html

• MATLAB release: MATLAB 7.5 (R2007b)