Conventional wisdom dictates that learning rate should be in the stable regime so gradient-based algorithms don't blow up. This letter introduces a simple scenario where an unstably large scheme leads to super fast convergence, with convergence depending only logarithmically on condition number of problem. Our uses Cyclical Learning Rate we periodically take one unstable step and several small ...

This paper proposes a new algorithm using a maximum neural network model to k-color vertices of a simple undirected graph. Unlike traditional neural nets, the proposed network is guaranteed to have 100% convergence rate to valid solutions with no parameter tuning needed. The power of the new method to solve this NP-complete problem will be shown in a number of simulations.

We derive a bound on the order of accuracy for interpolation schemes used in energy stable summation-by-parts discretizations on non-conforming multiblock grids. This result explains the suboptimal accuracy of such schemes reported in previous works. Numerical simulations confirm a corresponding reduced convergence rate in both maximum and L2 norms.

In this paper, the higher-order asymptotic expansion of the moment of extreme from generalized Maxwell distribution is gained, by which one establishes the rate of convergence of the moment of the normalized partial maximum to the moment of the associate Gumbel extreme value distribution.

Let {Xn, n ≥ 1} be an independent and identically distributed random sequence with common distribution F obeying the lognormal distribution. In this paper, we obtain the exact uniform convergence rate of the distribution of the maximum to its extreme value limit under power normalization. Mathematics Subject Classification(2010). Primary 62E20, 60E05; Secondary 60F15, 60G15.