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141.
A two-step modulus-based multisplitting iteration method for the nonlinear complementarity problem 下载免费PDF全文
In this paper, we construct a two-step modulus-based multisplitting iteration method based on multiple splittings of the system matrix for the nonlinear complementarity problem. And we prove its convergence when the system matrix is an $H$-matrix with positive diagonal elements. Numerical experiments show that the proposed method is efficient. 相似文献
142.
A proximal gradient descent method for the extended second-order cone linear complementarity problem
We consider an extended second-order cone linear complementarity problem (SOCLCP), including the generalized SOCLCP, the horizontal SOCLCP, the vertical SOCLCP, and the mixed SOCLCP as special cases. In this paper, we present some simple second-order cone constrained and unconstrained reformulation problems, and under mild conditions prove the equivalence between the stationary points of these optimization problems and the solutions of the extended SOCLCP. Particularly, we develop a proximal gradient descent method for solving the second-order cone constrained problems. This method is very simple and at each iteration makes only one Euclidean projection onto second-order cones. We establish global convergence and, under a local Lipschitzian error bound assumption, linear rate of convergence. Numerical comparisons are made with the limited-memory BFGS method for the unconstrained reformulations, which verify the effectiveness of the proposed method. 相似文献
143.
Zhong‐Zhi Bai 《Numerical Linear Algebra with Applications》2010,17(6):917-933
For the large sparse linear complementarity problems, by reformulating them as implicit fixed‐point equations based on splittings of the system matrices, we establish a class of modulus‐based matrix splitting iteration methods and prove their convergence when the system matrices are positive‐definite matrices and H+‐matrices. These results naturally present convergence conditions for the symmetric positive‐definite matrices and the M‐matrices. Numerical results show that the modulus‐based relaxation methods are superior to the projected relaxation methods as well as the modified modulus method in computing efficiency. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
144.
Recently, filter methods are extensively studied to handle nonlinear programming problems. Because of good numerical results, filter techniques are attached importance to. The nonlinear complementarity problem can be reformulated as the least l2-norm solution of an optimization problem. In this paper, basing on the filter technique and the new smoothing function, we present a new Filter-Levenberg-Marquardt method for solving the equation system with the disturbance . Under the assumption that the lever set of the problem is compact, we prove its global convergence. 相似文献
145.
Tie Ni 《Applied mathematics and computation》2010,216(7):2207-3378
The smoothing-type algorithm has been successfully applied to solve various optimization problems. In general, the smoothing-type algorithm is designed based on some monotone line search. However, in order to achieve better numerical results, the non-monotone line search technique has been used in the numerical computations of some smoothing-type algorithms. In this paper, we propose a smoothing-type algorithm for solving the nonlinear complementarity problem with a non-monotone line search. We show that the proposed algorithm is globally and locally superlinearly convergent under suitable assumptions. The preliminary numerical results are also reported. 相似文献
146.
S.Z. Németh 《Applied mathematics and computation》2010,217(5):2184-2190
The notion of exceptional family of elements for general order complementarity problems in Banach spaces will be introduced. It will be shown that for general order complementarity problems defined by completely continuous fields the problem has either a solution or an exceptional family of elements. Finite dimensional examples and an application to integral operators will be given. 相似文献
147.
In this article, we investigate robust optimization equilibria with two players, in which each player can neither evaluate his opponent's strategy nor his own cost matrix accurately while may estimate a bounded set of the strategy or cost matrix. We obtain a result that solving this equilibria can be formulated as solving a second-order cone complementarity problem under an ellipsoid uncertainty set or a mixed complementarity problem under a box uncertainty set. We present some numerical results to illustrate the behaviour of robust optimization equilibria. 相似文献
148.
149.
A new predictor-corrector algorithm is proposed for solvingP
*(κ)-matrix linear complementarity problems. If the problem is solvable, then the algorithm converges from an arbitrary positive
starting point (x
0,s
0). The computational complexity of the algorithm depends on the quality of the starting point. If the starting point is feasible
or close to being feasible, it has
-iteration complexity, whereρ
0 is the ratio of the smallest and average coordinate ofX
0
s
0. With appropriate initialization, a modified version of the algorithm terminates in O((1+κ)2(n/ρ
0)L) steps either by finding a solution or by determining that the problem has no solution in a predetermined, arbitrarily large,
region. The algorithm is quadratically convergent for problems having a strictly complementary solution. We also propose an
extension of a recent algorithm of Mizuno toP
*(κ)-matrix linear complementarity problems such that it can start from arbitrary positive points and has superlinear convergence
without a strictly complementary condition.
The work of this author was supported in part by NSF, Grant DMS 9305760 and by an Oberman fellowship from the University of
Iowa Center for Advanced Studies. 相似文献
150.
A large-step infeasible path-following method is proposed for solving general linear complementarity problems with sufficient matrices. If the problem has a solution, the algorithm is superlinearly convergent from any positive starting points, even for degenerate problems. The algorithm generates points in a large neighborhood of the central path. Each iteration requires only one matrix factorization and at most three (asymptotically only two) backsolves. It has been recently proved that any sufficient matrix is a P
*()-matrix for some 0. The computational complexity of the algorithm depends on as well as on a feasibility measure of the starting point. If the starting point is feasible or close to being feasible, then the iteration complexity is
. Otherwise, for arbitrary positive and large enough starting points, the iteration complexity is O((1 + )2
nL). We note that, while computational complexity depends on , the algorithm itself does not. 相似文献