1,281 research outputs found
A New Optimal Stepsize For Approximate Dynamic Programming
Approximate dynamic programming (ADP) has proven itself in a wide range of
applications spanning large-scale transportation problems, health care, revenue
management, and energy systems. The design of effective ADP algorithms has many
dimensions, but one crucial factor is the stepsize rule used to update a value
function approximation. Many operations research applications are
computationally intensive, and it is important to obtain good results quickly.
Furthermore, the most popular stepsize formulas use tunable parameters and can
produce very poor results if tuned improperly. We derive a new stepsize rule
that optimizes the prediction error in order to improve the short-term
performance of an ADP algorithm. With only one, relatively insensitive tunable
parameter, the new rule adapts to the level of noise in the problem and
produces faster convergence in numerical experiments.Comment: Matlab files are included with the paper sourc
Postprocessed integrators for the high order integration of ergodic SDEs
The concept of effective order is a popular methodology in the deterministic
literature for the construction of efficient and accurate integrators for
differential equations over long times. The idea is to enhance the accuracy of
a numerical method by using an appropriate change of variables called the
processor. We show that this technique can be extended to the stochastic
context for the construction of new high order integrators for the sampling of
the invariant measure of ergodic systems. The approach is illustrated with
modifications of the stochastic -method applied to Brownian dynamics,
where postprocessors achieving order two are introduced. Numerical experiments,
including stiff ergodic systems, illustrate the efficiency and versatility of
the approach.Comment: 21 pages, to appear in SIAM J. Sci. Compu
Hamevol1.0: a C++ code for differential equations based on Runge-Kutta algorithm. An application to matter enhanced neutrino oscillation
We present a C++ implementation of a fifth order semi-implicit Runge-Kutta
algorithm for solving Ordinary Differential Equations. This algorithm can be
used for studying many different problems and in particular it can be applied
for computing the evolution of any system whose Hamiltonian is known. We
consider in particular the problem of calculating the neutrino oscillation
probabilities in presence of matter interactions. The time performance and the
accuracy of this implementation is competitive with respect to the other
analytical and numerical techniques used in literature. The algorithm design
and the salient features of the code are presented and discussed and some
explicit examples of code application are given.Comment: 18 pages, Late
A symmetry-adapted numerical scheme for SDEs
We propose a geometric numerical analysis of SDEs admitting Lie symmetries
which allows us to individuate a symmetry adapted coordinates system where the
given SDE has notable invariant properties. An approximation scheme preserving
the symmetry properties of the equation is introduced. Our algorithmic
procedure is applied to the family of general linear SDEs for which two
theoretical estimates of the numerical forward error are established.Comment: A numerical example adde
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