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1.
The behavior of the equioscillation points (alternants) for the error in best uniform approximation on [–1, 1] by rational functions of degreen is investigated. In general, the points of the alternants need not be dense in [–1, 1], even when approximation by rational functions of degree (m, n) is considered and asymptoticallym/n 1. We show, however, that if more thanO(logn) poles of the approximants stay at a positive distance from [–1, 1], then asymptotic denseness holds, at least for a subsequence. Furthermore, we obtain stronger distribution results when n (0 < 1) poles stay away from [–1, 1]. In the special case when a Markoff function is approximated, the distribution of the equioscillation points is related to the asymptotics for the degree of approximation.The research of this author was supported, in part, by NSF grant DMS 920-3659. 相似文献
2.
Summary Quasiperiodic solutions of perturbed integrable Hamiltonian equations such as weakly coupled harmonic oscillators can be found by constructing an appropriate coordinate transformation which leads to a small divisor problem. However the numerical difficulties are not merely caused by the small divisors but rather by the appearence of ghost solutions, which appear in any reasonable discretization of the problem. Our numerical treatment, based on a Newton-type iteration, guarantees an approximation of the relevant solution of the nonlinear problem. Numerical solutions are found up to a critical value of the coupling constant, which is much larger than the coupling constants allowed by the existence theory available so far. 相似文献
3.
Dietrich Braess 《Numerische Mathematik》1981,37(3):387-404
Summary The treatment of a multigrid method in the framework of numerical analysis elucidates that regularity of the solution is not necessary for the convergence of the multigrid algorithm but only for fast convergence. For the linear equations which arise from the discretization of the Poisson equation, a convergence factor 0,5 is established independent of the shape of the domain and of the regularity of the solution.Dedicated to Professor Dr.Dr.h.c. Lothar Collatz on the occasion of his 70 th birthday 相似文献
4.
The uniqueness of monosplines and perfect splines of leastL p-norm is treated in the framework of generalized monosplines and total positivity. The analysis is based on the invariance properties of the degree of a certain mapping and on a new composition result for totally positive kernels. For theL p-case 1<p<∞, uniqueness is shown under the same extra conditions as were previously shown to be needed in theL p-case. The uniqueness in theL ∞-case is obtained without any restrictions. 相似文献
5.
Dietrich Braess 《Numerische Mathematik》2005,101(3):415-421
We show that a posteriori estimators for the obstacle problem are easily obtained from the theory for linear equations. The
theory would be even simpler if the Lagrange multiplier does not have a nonconforming contribution as it has in actual finite
element computations. 相似文献
6.
Dietrich Braess 《Numerische Mathematik》1977,29(1):123-132
Summary The region of attraction of a zero of a polynomial consists of those points from which the Newton method may be started when this zero is to be computed. The regions of attraction are approximately characterized by studying a continuous analog of the Newton method. 相似文献
7.
A finite element method is considered for dealing with nearly incompressible material. In the case of large deformations the nonlinear character of the volumetric contribution has to be taken into account. The proposed mixed method avoids volumetric locking also in this case and is robust for (with being the well-known Lamé constant). Error estimates for the -norm are crucial in the control of the nonlinear terms.
8.
Dietrich Braess 《Aequationes Mathematicae》1974,10(1):118-119
Ohne Zusammenfassung 相似文献
9.
Ohne Zusammenfassung 相似文献
10.
When learning processes depend on samples but not on the order of the information in the sample, then the Bernoulli distribution is relevant and Bernstein polynomials enter into the analysis. We derive estimates of the approximation of the entropy function x log x that are sharper than the bounds from Voronovskaja's theorem. In this way we get the correct asymptotics for the Kullback–Leibler distance for an encoding problem. 相似文献