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991.
In high accuracy long-time integration of differential equations, round-off errors may dominate truncation errors. This article
studies the influence of round-off on the conservation of first integrals such as the total energy in Hamiltonian systems.
For implicit Runge–Kutta methods, a standard implementation shows an unexpected propagation. We propose a modification that
reduces the effect of round-off and shows a qualitative and quantitative improvement for an accurate integration over long
times.
AMS subject classification (2000) 65L06, 65G50, 65P10 相似文献
992.
Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the D4-Σd(D4-Σ1, D4-Σ2) symmetry-breaking bifurcation points on the branch of the D4 symmetric positive solutions are found via the extended systems. Finally, Σd(Σ1, Σ2) sym- metric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction. 相似文献
993.
For Principal Component Analysis in Reproducing Kernel Hilbert Spaces (KPCA), optimization over sets containing only linear
combinations of all n-tuples of kernel functions is investigated, where n is a positive integer smaller than the number of data. Upper bounds on the accuracy in approximating the optimal solution,
achievable without restrictions on the number of kernel functions, are derived. The rates of decrease of the upper bounds
for increasing number n of kernel functions are given by the summation of two terms, one proportional to n
−1/2 and the other to n
−1, and depend on the maximum eigenvalue of the Gram matrix of the kernel with respect to the data. Primal and dual formulations
of KPCA are considered. The estimates provide insights into the effectiveness of sparse KPCA techniques, aimed at reducing
the computational costs of expansions in terms of kernel units. 相似文献
994.
995.
996.
Ekkehard W. Sachs 《Mathematical Programming》1986,35(1):71-82
Broyden's method is formulated for the solution of nonlinear operator equations in Hilbert spaces. The algorithm is proven to be well defined and a linear rate of convergence is shown. Under an additional assumption on the initial approximation for the derivative we prove the superlinear rate of convergence. 相似文献
997.
The problem of the thermal stability of a horizontal incompressible fluid layer with linear and nonlinear temperature distributions is solved by using the sequential gradient-restoration algorithm developed for optimal control problems. The hydrodynamic boundary conditions for the layer include a rigid or free upper surface and a rigid lower surface. The resulting disturbing equations are solved as a Bolza problem in the calculus of variations. The results of the study are compared with the existing works in the literature.The authors acknowledge valuable discussions with Dr. A. Miele. 相似文献
998.
K. C. Kiwiel 《Journal of Optimization Theory and Applications》1986,48(3):437-449
This paper presents a method for minimizing the sum of a possibly nonsmooth convex function and a continuously differentiable function. As in the convex case developed by the author, the algorithm is a descent method which generates successive search directions by solving quadratic programming subproblems. An inexact line search ensures global convergence of the method to stationary points. 相似文献
999.
1000.
Zolfira Zakirova 《Czechoslovak Journal of Physics》2005,55(11):1541-1544
We study the six-dimensional pseudo-Riemannian spaces with two time-like coordinates that admit non-homothetic infinitesimal
projective transformations. The metrics are manifestly obtained and the projective group properties are determined. We also
find a generic definition of projective motion in the 6-dimensional rigid h-space.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005. 相似文献