45,100 research outputs found
Convergence properties of the effective interaction
The convergence properties of two perturbative schemes to sum the so-called
folded diagrams are critically reviewed, with an emphasis on the intruder state
problem. The methods we study are the approaches of Kuo and co-workers and Lee
and Suzuki. The suitability of the two schemes for shell-model calculations are
discussed.Comment: 10 pages in revtex ver. 3.0. 3 figs can be obtained upon request.
Univerisity of Oslo report UiO/PHYS/93-2
On Convergence Properties of Shannon Entropy
Convergence properties of Shannon Entropy are studied. In the differential
setting, it is shown that weak convergence of probability measures, or
convergence in distribution, is not enough for convergence of the associated
differential entropies. A general result for the desired differential entropy
convergence is provided, taking into account both compactly and uncompactly
supported densities. Convergence of differential entropy is also characterized
in terms of the Kullback-Liebler discriminant for densities with fairly general
supports, and it is shown that convergence in variation of probability measures
guarantees such convergence under an appropriate boundedness condition on the
densities involved. Results for the discrete setting are also provided,
allowing for infinitely supported probability measures, by taking advantage of
the equivalence between weak convergence and convergence in variation in this
setting.Comment: Submitted to IEEE Transactions on Information Theor
Pricing exotic options using strong convergence properties?
In finance, the strong convergence properties of discretisations of stochastic differential equations (SDEs) are very important for the hedging and valuation of exotic options. In this paper we show how the use of the Milstein scheme can improve the convergence of the multi-level Monte Carlo method, so that the computational cost to achieve an accuracy of O(e) is reduced to O() for a Lipschitz payoff. The Milstein scheme gives first order strong convergence for all 1âdimensional systems (one Wiener process). However, for processes with two or more Wiener processes, such as correlated portfolios and stochastic volatility models, there is no exact solution for the iterated integrals of second order (LĂ©vy area) and the Milstein scheme neglecting the LĂ©vy area gives the same order of convergence as the Euler-Maruyama scheme. The purpose of this paper is to show that if certain conditions are satisfied, we can avoid the calculation of the LĂ©vy area and obtain first convergence order by applying an orthogonal transformation. We demonstrate when the conditions of the 2âDimensional problem permit this and give an exact solution for the orthogonal transformation. We present examples of pricing exotic options to demonstrate that the use of both the orthogonal Milstein scheme and the Multi-level Monte Carlo give a substantial reduction in the computation cost
Convergence properties of simple genetic algorithms
The essential parameters determining the behaviour of genetic algorithms were investigated. Computer runs were made while systematically varying the parameter values. Results based on the progress curves obtained from these runs are presented along with results based on the variability of the population as the run progresses
Convergence of density-matrix expansions for nuclear interactions
We extend density-matrix expansions in nuclei to higher orders in derivatives
of densities and test their convergence properties. The expansions allow for
converting the interaction energies characteristic to finite- and short-range
nuclear effective forces into quasi-local density functionals. We also propose
a new type of expansion that has excellent convergence properties when
benchmarked against the binding energies obtained for the Gogny interaction.Comment: 4 pages, 3 figure
Some Convergence Properties of Broyden's Method
In 1965 Broyden introduced a family of algorithms called(rank-one) quasiĂąâŹâNew-ton methods for iteratively solving systems of nonlinear equations. We show that when any member of this family is applied to an n x n nonsingular system of linear equations and direct-prediction steps are taken every second iteration, then the solution is found in at most 2n steps. Specializing to the particular family member known as Broydenâs (good) method, we use this result to show that Broyden's method enjoys local 2n-step Q-quadratic convergence on nonlinear problems.
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