Epsilon Algorithm for Computing Padé Approximant

I am looking for a MATLAB implementation of the Epsilon Algorithm (theorem 1 from here). When I look at the Wikipedia page for Padé approximant, I find this quote: "For given x, Padé approximants can be computed by Wynn's epsilon algorithm[1]...". The Wikipedia article links to the epsilon algorithm paper. I am wondering if anyone has ran across this in MATLAB somewhere?

Answer 1

[Zezheng Wu]

Not sure whether you still need this but also for whoever wants to use Wynn's epsilon in MATLAB, here is the code:

function res = wynn(s)
  % Step 1: Check length of s and adjust if it's even
  n = length(s);
  if mod(n, 2) == 0
    s = s(1:end-1);
    n = n - 1;
  end

  % Step 2: Initialize the epsilon matrix A with s on the first column
  A = zeros(n, n);
  A(:, 1) = s;

  % Step 3: Compute the remaining columns using Wynn's method
  for j = 2:n
    for i = 1:(n - j + 1)
      if j == 2
        A(i, j) = 1 / (A(i + 1, j - 1) - A(i, j - 1));
      else
        A(i, j) = A(i + 1, j - 2) + 1 / (A(i + 1, j - 1) - A(i, j - 1));
      end
    end
  end

  % Step 4: Return the last element in the last column as the estimate of the limit
  res = A(1, n);
end

[Jason Nicholson]

Thank you.