In lapack library, there are many routines for computing eigenvalues. But now, I only want to konw the maximum and the minimum eigenvalues for a real symmetric, positive definite matrix, because In my program, I will compute the maximum and the minimum eigenvalues for many, many times. So, the time saving become a serious problem.
Many routines will need N^3 operations. So can you tell me whether the routines for this problem needed less operations are contained in lapack library?