سوال ۱۶ کنکور ارشد ریاضی ۱۴۰۰

PASSAGE 1 — Number of Steps, Work per Step, and Preconditioning (paragraph 1):

"Gaussian elimination, QR factorization, and most other algorithms of dense linear algebra fit the following pattern: there are $O(m)$ steps, each requiring $O(m^{2})$ work, for a total work estimate of $O(m^{3})$. (Of course these figures, especially the second, may change on a parallel computer.) For iterative methods, the same figures still apply, but now they represent a typical worst-case behavior. When these methods succeed, they may do so by reducing one or both of these factors."

Iterative methods of concern in the first paragraph require a total work -------------.