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On Numerical Solution of the Gardner–Ostrovsky Equation

M. A. Obregon, Y. A. Stepanyants (2012)

Mathematical Modelling of Natural Phenomena

A simple explicit numerical scheme is proposed for the solution of the Gardner–Ostrovsky equation (ut + cux + α uux + α1u2ux + βuxxx)x = γu which is also known as the extended rotation-modified Korteweg–de Vries (KdV) equation. This equation is used for the description of internal oceanic waves affected by Earth’ rotation. Particular versions of this equation with zero some of coefficients, α, α1, β, or γ are also known in numerous applications....

On the number of iterations required by Von Neumann addition

Rudolf Grübel, Anke Reimers (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We investigate the number of iterations needed by an addition algorithm due to Burks et al. if the input is random. Several authors have obtained results on the average case behaviour, mainly using analytic techniques based on generating functions. Here we take a more probabilistic view which leads to a limit theorem for the distribution of the random number of steps required by the algorithm and also helps to explain the limiting logarithmic periodicity as a simple discretization phenomenon.

On the number of iterations required by Von Neumann addition

Rudolf Grübel, Anke Reimers (2010)

RAIRO - Theoretical Informatics and Applications

We investigate the number of iterations needed by an addition algorithm due to Burks et al. if the input is random. Several authors have obtained results on the average case behaviour, mainly using analytic techniques based on generating functions. Here we take a more probabilistic view which leads to a limit theorem for the distribution of the random number of steps required by the algorithm and also helps to explain the limiting logarithmic periodicity as a simple discretization phenomenon.

On the randomized complexity of Banach space valued integration

Stefan Heinrich, Aicke Hinrichs (2014)

Studia Mathematica

We study the complexity of Banach space valued integration in the randomized setting. We are concerned with r times continuously differentiable functions on the d-dimensional unit cube Q, with values in a Banach space X, and investigate the relation of the optimal convergence rate to the geometry of X. It turns out that the nth minimal errors are bounded by c n - r / d - 1 + 1 / p if and only if X is of equal norm type p.

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