Accuracy of principal Eigen vector and Eigen value estimates

Hi,

I am writing a small piece of software that will use the AHP method ("Analytic Hierarchy Process (AHP) is a structured technique for dealing with complex decisions"). This requires calculating principal Eigen vectors and Eigen values.

Since I don't have a mathematics background, I found this great tutorial:

Analytic Hierarchy Process AHP Tutorial

The methods used to calculate the principal Eigen vector and Eigen value in that tutorial are only approximations. I wanted to ask if you guys have any idea as to how accurate these approximations are as the matrix size grows beyond 3x3 (i.e. would using the approximation method be sufficient?).

Any help would be much appreciated.