I am studying a paper as "homework" for a class involving numerical analysis. It is required to write a MATLAB code that does the sperimentation the paper studies. Luckily in this paper there are suggested values and the number of iterations required to achieve a precision of $10^{-20}$ (it is about conjugate gradient method and a particular preconditioner, by the way). There are two things that worry me: First, the number of iterations I need are a bit more than those reported, like 2 or three times more, but that shouldn't be a very big problem. The real issue is that I only have acceptable results for a precision of $10^{-15}$. If I wanted a solution with error bounded in norm by $10^{-20}$, the algorithm can go for even 1000 iterations without going less than $10^{-15}$
Since the numbers on the matrices are obtained by using Euler's gamma function and Beta function, I was wondering if there was a problem of truncation error in matlab. I have found only suggestions about using commands like vpa or digits, but it seems those are referred to a single operation, while I want matlab to be more precise on the whole function. Is there aa way to do this?