My research activity involves the development of solvers for stiff system of equations on the basis of explicit methods of numerical integration.

One bottleneck of my approach is the identification of the eigen-system at each integration time step, which is clearly a very computationally demanding task.

However, the set of eigenvectors varies smoothly with time.

Therefore, I am expecting that the convergence of any iterative method (power method, QR, …) to find the eigensystem might be enhanced if one could start the iterative procedure using the eigenvectors of the previous time step as first guess, as in a continuation method.

After many years of unsuccessful attempts to find any one routine (such as DGEEV) that will allow the user to prescribe the first guess, I eventually decided to invoke your expert advise on this regard.

My questions are:

1) in your experience, could you tell if the cost to find the eigensystem will indeed be lower if the initial guess is very close to the correct answer ?

2) do you know if there exists a routine (such as DGEEV), where one can prescribe the first guess in the iterative process to find the eigensystem of a certain matrix J ?

3) if such a routine does not exist yet, how difficult would be to modify DGEEV according to this my request?

I would really very much appreciate any help you could provide on this matter.