The Helmholtz equation is considered. The matrices decomposition algorithms for Legendre spectral collocation approximation, which nearly reduce a half of scale for original discrete system, are achieved by the centrosymmetry and positivity. Also, the di erence and finite element preconditioning...

We consider the basic problem of refi tting a time series over a finite period of time and formulate it as a stochastic dynamic program. By changing the underlying Markov decision process we are able to obtain a model that at optimality considers historical data as well as forecasts of future...