Tbis paper describes a preconditioned conjugate gradient method tbat can be effectively implemented on both vector machines and parallel arrays to solve sparse symmetric and positive definite systema of linear equations. The implementation on the CYBER 203/205 and on tbe Finite Element Machine is discuased and result a obtained using the method on these machines are siven.

Dyna planning is an efficient way of learning from real and imaginary experience. Existing tabular and linear Dyna algorithms are single-step, because an “imaginary” feature is predicted only one step into the future. In this paper, we introduce a multi-step Dyna planning that predicts more steps into the future. Multi-step Dyna is able to figure out a sequence of multi-step results when a real...

The Shipboard Automatic Identification System (AIS) is crucial for navigation safety and maritime surveillance, data mining and pattern analysis of AIS information have attracted considerable attention in terms of both basic research and practical applications. Clustering of spatio-temporal AIS trajectories can be used to identify abnormal patterns and mine customary route data for transportati...

We construct optimal k-step, 5to 10-stage, explicit, strong-stability-preserving Hermite-Birkhoff (SSP HB) methods of order 12 with nonnegative coefficients by combining linear k-step methods of order 9 with 5to 10-stage Runge-Kutta (RK) methods of order 4. Since these methods maintain the monotonicity property, they are well suited for solving hyperbolic PDEs by the method of lines after a spa...

We now discuss the theory of fixed–order constant–step–size linear multistep methods. This classical theory is presented in [HNW93] Sect. III.1–4 (nons-tiff) and [HW96] Sect. V.1 (stiff), as well as [Gea71] Chap. 7, [Lam91] Chap. 3, [Sha94] Chap. 4, and many other sources. While multistep methods are rarely used in practice with fixed order and constant step size, this theory is useful because ...

We apply the dressing method to a string solution given by a static string wrapped around the equator of a three-sphere and find that the result is the single spike solution recently discussed in the literature. Further application of the method allows the construction of solutions with multiple spikes. In particular we construct the solution describing the scattering of two single spikes and c...

the solutions of mathematical models for the estimation of the kinetic, and biokinetic parameters of naphthalene, anthracene and pyrene during degradation in surface and subsurface soils are presented in this work. the models were developed using the twin concepts of rate-determining step and steady-state approximation method. they described the biodegradation of single and a mixture of polycy...

This paper establishes the higher-order equivalence of the k-step bootstrap, introduced recently by Davidson and MacKinnon (1999), and the standard bootstrap. The k-step bootstrap is a very attractive alternative computationally to the standard bootstrap for statistics based on nonlinear extremum estimators, such as generalized method of moment and maximum likelihood estimators. The paper also ...