Search results for "Convergence tests"
showing 7 items of 7 documents
Global convergence and rate of convergence of a method of centers
1994
We consider a method of centers for solving constrained optimization problems. We establish its global convergence and that it converges with a linear rate when the starting point of the algorithm is feasible as well as when the starting point is infeasible. We demonstrate the effect of the scaling on the rate of convergence. We extend afterwards, the stability result of [5] to the infeasible case anf finally, we give an application to semi-infinite optimization problems.
Iterative approximation to a coincidence point of two mappings
2015
In this article two methods for approximating the coincidence point of two mappings are studied and moreover, rates of convergence for both methods are given. These results are illustrated by several examples, in particular we apply such results to study the convergence and their rate of convergence of these methods to the solution of a nonlinear integral equation and of a nonlinear differential equation.
Free-surface flows solved by means of SPH schemes with numerical diffusive terms
2010
A novel system of equations has been defined which contains diffusive terms in both the continuity and energy equations and, at the leading order, coincides with a standard weakly-compressible SPH scheme with artificial viscosity. A proper state equation is used to associate the internal energy variation to the pressure field and to increase the speed of sound when strong deformations/compressions of the fluid occur. The increase of the sound speed is associated to the shortening of the time integration step and, therefore, allows a larger accuracy during both breaking and impact events. Moreover, the diffusive terms allows reducing the high frequency numerical acoustic noise and smoothing …
The Random-Time Binomial Model
1999
In this paper we study Binomial Models with random time steps. We explain, how calculating values for European and American Call and Put options is straightforward for the Random-Time Binomial Model. We present the conditions to ensure weak-convergence to the Black-Scholes setup and convergence of the values for European and American put options. Differently to the CRR-model the convergence behaviour is extremely smooth in our model. By using extrapolation we therefore achieve order of convergence two. This way it is an efficient tool for pricing purposes in the Black-Scholes setup, since the CRR model and its extrapolations typically achieve order one. Moreover our model allows in a straig…
A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH
2009
In literature, it is well know that the Smoothed Particle Hydrodynamics method can be affected by numerical noise on the pressure field when dealing with liquids. This can be highly dangerous when an SPH code is dynamically coupled with a structural solver. In this work a simple procedure is proposed to improve the computation of the pressure distribution in the dynamics of liquids. Such a procedure is based on the use of a density diffusion term in the equation for the mass conservation. This diffusion is a pure numerical effect, similar to the well known artificial viscosity originally proposed in SPH method to smooth out the shock discontinuities. As the artificial viscosity, the density…
On the Convergence of Formal Integrals in Finite Time
1982
Consider a differential system: x = f (x) + e g(x), \(x \in {R^n}.\). Let h(x) = ho(x) + eh1 (x)... a “third” integral. For finite time t, I obtain an eo such that the series h(x) converges if e > eo. When t tends to infinite, eo tends to zero.
An algorithm for computing geometric relative velocities through Fermi and observational coordinates
2013
We present a numerical method for computing the \textit{Fermi} and \textit{observational coordinates} of a distant test particle with respect to an observer. We apply this method for computing some previously introduced concepts of relative velocity: \textit{kinematic}, \textit{Fermi}, \textit{spectroscopic} and \textit{astrometric} relative velocities. We also extend these concepts to non-convex normal neighborhoods and we make some convergence tests, studying some fundamental examples in Schwarzschild and Kerr spacetimes. Finally, we show an alternative method for computing the Fermi and astrometric relative velocities.