function val=AitkenMethod(a,steps,object,display)
% function S = AitkenMethod(a,steps,object,display)
%
% extrapolates a sequence or series by using 
% Aitkens Delta^2 method
%
% a         vector of terms 
% steps     number of extrapolation steps 
%           (method needs 2*steps+1 elements of a)
% object    'sequence': extrapolation to the limit of a
%           'series'  : extrapolation to the limit of cumsum(a)
% display   'on': plot the absolute value of differences in the first
%           row of the extrapolation table for diagnosis
%
% S         extrapolatd value

% Vektor a als Spaltenvektor anpassen
dims = size(a);
if dims(1) == 1
    a = a';
end

S=zeros(length(a),steps+1);
switch object
    case 'sequence'
        S(:,1)=a;
    case 'series'
        S(:,1)=cumsum(a);
    otherwise
        error('MATLAB:badopt','%s: no such object known',object);
end
for j=2:steps+1
    d2=diff(S(2:end-2*j+4,j-1));
    d1=diff(S(1:end-2*j+3,j-1));
    r=d2./d1;
    fac=r./(1-r);
    S(1:end-2*j+2,j)=S(3:end-2*j+4,j-1)+fac.*d2;
end
if isequal(display,'on')
    h=semilogy(1:length(S(1,:))-1,abs(diff(S(1,:))));
    set(h,'LineWidth',3);
end
S;
val=S(1,end);
return