I am trying to compute the Moore- Penrose inverse of a given $m\times n$ matrix $A$. I did convergence analysis then I came across to the following condition.
For convergence of my method: $\max\mid 1 - \lambda_\max(X_0 A))\mid <1$ where $X_{0}$ is an $n\times m$ matrix and is the initial approximation for my sequence of iterations to compute Moore- Penrose inverse and $\lambda$ stands for eigenvalue of a matrix.
My question is how could I choose $X_{0}$ so that this condition $\max\mid 1 - eigenvalue(X_0 A))\mid <1$ holds true.
I know one possibility that is to choose $X_{0} = \alpha A^t$ and $0<\alpha<2/\lambda_\max(AA^t)$, and for that
But I need any other alternate possibility. I need help with this. please help me. I would be very much thankful.