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We build upon the recent papers by Weinstein and Yu (FOCS'16), Larsen(FOCS'12), and Clifford et al. (FOCS'15) to present a general framework thatgives amortized lower bounds on the update and query times of dynamic datastructures. Using our framework, we present two concrete results.  (1) For the dynamic polynomial evaluation problem, where the polynomial isdefined over a finite field of size $n^{1+\Omega(1)}$ and has degree $n$, anydynamic data structure must either have an amortized update time of$\Omega((\lg n/\lg \lg n)^2)$ or an amortized query time of $\Omega((\lg n/\lg\lg n)^2)$.  (2) For the dynamic online matrix vector multiplication problem, where we getan $n \times n$ matrix whose entires are drawn from a finite field of size$n^{\Theta(1)}$, any dynamic data structure must either have an amortizedupdate time of $\Omega((\lg n/\lg \lg n)^2)$ or an amortized query time of$\Omega(n \cdot (\lg n/\lg \lg n)^2)$.  For these two problems, the previous works by Larsen (FOCS'12) and Cliffordet al. (FOCS'15) gave the same lower bounds, but only for worst case update andquery times. Our bounds match the highest unconditional lower bounds known tilldate for any dynamic problem in the cell-probe model.

New Amortized Cell-Probe Lower Bounds for Dynamic Problems