Metric tensor as the dynamical variable for variable-cell-shape molecular dynamics

Reduced Variable Molecular Dynamics

This article describes an extension to previously developed constraint techniques. These enhanced constraint methods will enable the study of large computational chemistry problems that cannot be easily handled with current constrained molecular dynamics (MD) methods. These methods are based on an O( N solution to the constrained equations of motion. The benefits of this approach are that (1) t...

Variable Metric Method for Minimization

The use of radial basis functions by variable shape parameter for solving partial differential equations

In this paper, some meshless methods based on the local Newton basis functions are used to solve some time dependent partial differential equations. For stability reasons, used variably scaled radial kernels for constructing Newton basis functions. In continuation, with considering presented basis functions as trial functions, approximated solution functions in the event of spatial variable wit...

Tensor decompositions for learning latent variable models

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models—including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation—which exploits a certain tensor structure in their low-order observable moments (typically, of secondand third-order). Specifically, parameter estimation is reduced to the...

On Variable - Metric Methods for Sparse Hessians

The relationship between variable-metric methods derived by norm minimization and those derived by symmetrization of rank-one updates for sparse systems is studied, and an analogue of Dennis's nonsparse symmetrization formula derived. A new method of using norm minimization to produce a sparse analogue of any nonsparse variable-metric method is proposed. The sparse BFGS generated by this method...