Multiple time stepping can be applied to the leapfrog/Stt ormer/Verlet integrator so as to eeect variable stepsize. The strategy maintains the symplecticness, time-reversibility, and second-order accuracy of leapfrog. This method can be applied to pairwise interactions by partitioning them into distance classes and smoothly decomposing the potential energy into the sum of potential energy funct...

The most widely used algorithm for training multiplayer feedforward networks, Error BackPropagation (EBP), is an iterative gradient descend algorithm by nature. Variable stepsize is the key to fast convergence of BP networks. A new optimal stepsize algorithm is proposed for accelerating the training process. It modifies the objective function to reduce the computational complexity of the Jacobi...

in this paper, we consider the construction of a new class ofnumerical methods based on the backward differentiation formulas(bdfs) that be equipped by including two off--step points. werepresent these methods from general linear methods (glms) pointof view which provides an easy process to improve their stabilityproperties and implementation in a variable stepsize mode. thesesuperiorities are ...

In this paper, we consider the construction of a new class of numerical methods based on the backward differentiation formulas (BDFs) that be equipped by including two off--step points. We represent these methods from general linear methods (GLMs) point of view which provides an easy process to improve their stability properties and implementation in a variable stepsize mode. These superioritie...

Some previous works show that symmetric fixedand variablestepsize linear multistep methods for second-order systems which do not have any parasitic root in their first characteristic polynomial give rise to a slow error growth with time when integrating reversible systems. In this paper, we give a technique to construct variable-stepsize symmetric methods from their fixed-stepsize counterparts,...