By Ivan Dimov, Stefka Fidanova, Ivan Lirkov
This booklet constitutes the completely refereed post-conference complaints of the eighth foreign convention on Numerical equipment and functions, NMA 2014, held in Borovets, Bulgaria, in August 2014. The 34 revised complete papers provided have been rigorously reviewed and chosen from fifty six submissions for inclusion during this publication. The papers are geared up within the following topical sections: Monte Carlo and quasi-Monte Carlo equipment; metaheuristics for optimization difficulties; complicated numerical equipment for medical computing; complex numerical innovations for PDEs and purposes; fixing huge engineering and medical issues of complex mathematical types; numerical simulations and again research in civil and mechanical engineering.
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Additional info for Numerical Methods and Applications: 8th International Conference, NMA 2014, Borovets, Bulgaria, August 20-24, 2014, Revised Selected Papers
Theorem 10. Assume that (23) holds. Then H−q ≥ 0 is a necessary condition for Ek = r(kH) ≥ 0 for large k. If H−q > 0, then Ek = r(kH) > 0 for large k. Proof. Both statements of the theorem follow since, by (23), Ek = ck −q (H−q + O(k −1 )), as k → ∞. (24) 22 V. Thom´ee The result shows, in particular, that Ek = r02 (kH) > 0 for large k if H−2 > 0. We complete this section by showing that for this method, the negative conclusion of Theorem 8 holds also for the LM method, even though M is then diagonal, under the not very restrictive assumption that Th is 4-connected in the following sense: There exists a path P in Zh consisting of four connected edges Pm Pn , with smn = 0, and such that the endpoints Pi , Pj of the path cannot be connected by a path with fewer than four edges.
2. Comparison of wave packets evolved for 100 fs using an optimized regeneration scheme and the conventional regeneration process; analytical solution shown by the solid line. g. a 32 P. Ellinghaus et al. 2 50 25 0 5 -2 0 -5 x-position [nm] Fig. 3. Comparison of wave packets evolved for 100 fs using regeneration schemes based on a Gaussian distribution and a mean with uniform distribution (as in Fig. 2); the analytical solution is shown for comparison. Gaussian distribution. The result, shown in Fig.
The problem of balancing of the errors is closely connected with the problem of obtaining an optimal ratio between the number of realizations N of the random variable and the mean value k of the number of steps in each random trajectory . The problem of balancing of both systematic and stochastic error is very important when Monte Carlo algorithms are used. The balancing of errors (both, systematic and stochastic) allows to get an approximation of the quantity of interest in the most eﬃcient way by ﬁxing the number of samples N and the number of iterations k if the error is ﬁxed.
Numerical Methods and Applications: 8th International Conference, NMA 2014, Borovets, Bulgaria, August 20-24, 2014, Revised Selected Papers by Ivan Dimov, Stefka Fidanova, Ivan Lirkov