共查询到20条相似文献,搜索用时 15 毫秒
1.
Kimmo I. Rosenthal 《Topology and its Applications》1982,13(2):167-176
In this paper, we investigate the concept of local equivalence relation, a notion suggested by Grothendieck. A local equivalence relation on a topological space X is a global section of the sheaf of germs of equivalence relations on X. We investigate the extent to which a local equivalence relation can be described by a global one and analogously when can a global equivalence relation be recovered from its associated local one. We also look at the notion of a fiber map, which sheds further light on these concepts. A motivating example is that of a foliation on a manifold. 相似文献
2.
Ioannis K. Argyros 《Journal of Applied Mathematics and Computing》2001,8(2):253-268
Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods.
The first uses conditions on the first Fréchet-derivative whereas the second theorem employs hypotheses on themth (m ≥ 2 an integer). Radius of convergence as well as rate of convergence results are derived. Results involving superlinear
convergence and known to be true for inexact Newton methods are extended here. Moreover, we show that under hypotheses on
the mth Fréchet-derivative our radius of convergence can sometimes be larger than the corresponding one in [10]. This allows
a wider choice for the initial guess. A numerical example is also provided to show that our radius of convergence is larger
than the one in [10]. 相似文献
3.
4.
Ivar Lie 《BIT Numerical Mathematics》1990,30(1):126-144
Multistep collocation methods for initial value problems in ordinary differential equations are known to be a subclass of multistep Runge-Kutta methods and a generalisation of the well-known class of one-step collocation methods as well as of the one-leg methods of Dahlquist. In this paper we derive an error estimation method of embedded type for multistep collocation methods based on perturbed multistep collocation methods. This parallels and generalizes the results for one-step collocation methods by Nørsett and Wanner. Simple numerical experiments show that this error estimator agrees well with a theoretical error estimate which is a generalisation of an error estimate first derived by Dahlquist for one-leg methods. 相似文献
5.
6.
The purpose of this paper is to propose and study local spline approximation methods for singular product integration, for
which; i) the precision degree is the highest possible using spline approximation; ii) the nodes can be assumed equal to arbitrary
points, where the integrand function f is known; iii) the number of the requested evaluations of f at the nodes is low; iv)
a satis factory convergence theory can be proved.
Work sponsored by “Ministero dell' University” and CNR of Italy 相似文献
7.
We study local convergence of quasi-Newton methods for solving systems of nonlinear equations defined by B-differentiable functions. We extend the classical linear and superlinear convergence results for general quasi-Newton methods as well as for Broyden's method. We also show how Broyden's method may be applied to nonlinear complementarity problems and illustrate its computational performance on two small examples. 相似文献
8.
In this paper, a theoretical method is presented to select fuzzy implication operators for the fuzzy inference sentence “if
x is A, then y is B”. By applying representation theorems, thirty-two fuzzy implication operators are obtained. It is shown that the obtained
operators are generalizations of classical inference rule A → B, A
c
→ B, A → B
c
and A
c
→ B
c
respectively and can be divided into four classes. By discussion, it is found that thirty of them among 420 fuzzy implication
operators presented by Li can be derived by applying representation theorems and another two new ones are obtained by the
use of our methods. 相似文献
9.
Tapio Pahikkala Willem Waegeman Evgeni Tsivtsivadze Tapio Salakoski Bernard De Baets 《European Journal of Operational Research》2010
In different fields like decision making, psychology, game theory and biology, it has been observed that paired-comparison data like preference relations defined by humans and animals can be intransitive. Intransitive relations cannot be modeled with existing machine learning methods like ranking models, because these models exhibit strong transitivity properties. More specifically, in a stochastic context, where often the reciprocity property characterizes probabilistic relations such as choice probabilities, it has been formally shown that ranking models always satisfy the well-known strong stochastic transitivity property. Given this limitation of ranking models, we present a new kernel function that together with the regularized least-squares algorithm is capable of inferring intransitive reciprocal relations in problems where transitivity violations cannot be considered as noise. In this approach it is the kernel function that defines the transition from learning transitive to learning intransitive relations, and the Kronecker-product is introduced for representing the latter type of relations. In addition, we empirically demonstrate on two benchmark problems, one in game theory and one in theoretical biology, that our algorithm outperforms methods not capable of learning intransitive reciprocal relations. 相似文献
10.
Mathematical Programming - In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear... 相似文献
11.
Gennady Yu. Kulikov 《Numerical Algorithms》2010,53(2-3):321-342
In this paper we discuss the theory of one-step extrapolation methods applied both to ordinary differential equations and to index 1 semi-explicit differential-algebraic systems. The theoretical background of this numerical technique is the asymptotic global error expansion of numerical solutions obtained from general one-step methods. It was discovered independently by Henrici, Gragg and Stetter in 1962, 1964 and 1965, respectively. This expansion is also used in most global error estimation strategies as well. However, the asymptotic expansion of the global error of one-step methods is difficult to observe in practice. Therefore we give another substantiation of extrapolation technique that is based on the usual local error expansion in a Taylor series. We show that the Richardson extrapolation can be utilized successfully to explain how extrapolation methods perform. Additionally, we prove that the Aitken-Neville algorithm works for any one-step method of an arbitrary order s, under suitable smoothness. 相似文献
12.
13.
Summary. In this paper, global optimization (GO) Lipschitz problems are considered where the multi-dimensional multiextremal objective
function is determined over a hyperinterval. An efficient one-dimensional GO method using local tuning on the behavior of
the objective function is generalized to the multi-dimensional case by the diagonal approach using two partition strategies.
Global convergence conditions are established for the obtained diagonal geometric methods. Results of a wide numerical comparison
show a strong acceleration reached by the new methods working with estimates of the local Lipschitz constants over different
subregions of the search domain in comparison with the traditional approach.
Received July 13, 2001 / Revised version received March 14, 2002 / Published online October 29, 2002
Mathematics Subject Classification (1991): 65K05, 90C30
Correspondence to: Yaroslav D. Sergeyev 相似文献
14.
Trond Steihaug 《Mathematical Programming》1983,27(2):176-190
Least change secant updates can be obtained as the limit of iterated projections based on other secant updates. We show that
these iterated projections can be terminated or truncated after any positive number of iterations and the local and the superlinear
rate of convergence are still maintained. The truncated iterated projections method is used to find sparse and symmetric updates
that are locally and superlinearly convergent.
A part of this paper was presented at the Third International Workshop on Numerical Analysis, IIMAS, University of Mexico,
January 1981 and ORSA-TIMS National Meeting, Houston, October 1981. 相似文献
15.
Tensor methods for nonlinear equations base each iteration upon a standard linear model, augmented by a low rank quadratic term that is selected in such a way that the mode is efficient to form, store, and solve. These methods have been shown to be very efficient and robust computationally, especially on problems where the Jacobian matrix at the root has a small rank deficiency. This paper analyzes the local convergence properties of two versions of tensor methods, on problems where the Jacobian matrix at the root has a null space of rank one. Both methods augment the standard linear model by a rank one quadratic term. We show under mild conditions that the sequence of iterates generated by the tensor method based upon an ideal tensor model converges locally and two-step Q-superlinearly to the solution with Q-order 3/2, and that the sequence of iterates generated by the tensor method based upon a practial tensor model converges locally and three-step Q-superlinearly to the solution with Q-order 3/2. In the same situation, it is known that standard methods converge linearly with constant converging to 1/2. Hence, tensor methods have theoretical advantages over standard methods. Our analysis also confirms that tensor methods converge at least quadratically on problems where the Jacobian matrix at the root is nonsingular.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.Research supported by AFOSR grant AFOSR-90-0109, ARO grant DAAL 03-91-G-0151, NSF grants CCR-8920519 CCR-9101795. 相似文献
16.
The effect of using a nonsymmetric and nonpositive-definite matrix for approximation of the Hessian inverse in unconstrained optimization is investigated. To this end, a new algorithm, which may be viewed as a member of the Huang family, is derived. The proposed algorithm possesses the quadratic termination property without exact line search. It seems from the numerical results that it is not essential to use a symmetric and positive-definite matrix. 相似文献
17.
Toufik Mansour 《Journal of Difference Equations and Applications》2013,19(6):555-563
In this paper, we solve several recurrence relations with two indices by using combinatorial methods. Moreover, we present several recurrence relations with two indices related to Dyck paths and Schröder paths. 相似文献
18.
Stephen J. Wright 《Mathematical Programming》1987,37(2):232-252
Methods for minimization of composite functions with a nondifferentiable polyhedral convex part are considered. This class
includes problems involving minimax functions and norms. Local convergence results are given for “active set” methods, in
which an equality-constrained quadratic programming subproblem is solved at each iteration. The active set consists of components
of the polyhedral convex function which are active or near-active at the current iteration. The effects of solving the subproblem
inexactly at each iteration are discussed; rate-of-convergence results which depend on the degree of inexactness are given. 相似文献
19.
《Optimization》2012,61(8):1153-1171
In Gonzaga et al. [A globally convergent filter method for nonlinear programming, SIAM J. Optimiz. 14 (2003), pp. 646–669] we discuss general conditions to ensure global convergence of inexact restoration filter algorithms for non-linear programming. In this article we show how to avoid the Maratos effect by means of a second-order correction. The algorithms are based on feasibility and optimality phases, which can be either independent or not. The optimality phase differs from the original one only when a full Newton step for the tangential minimization of the Lagrangian is efficient but not acceptable by the filter method. In this case a second-order corrector step tries to produce an acceptable point keeping the efficiency of the rejected step. The resulting point is tested by trust region criteria. Under the usual hypotheses, the algorithm inherits the quadratic convergence properties of the feasibility and optimality phases. This article includes a comparison between classical Sequential Quadratic Programming (SQP) and Inexact Restoration (IR) iterations, showing that both methods share the same asymptotic convergence properties. 相似文献
20.
In this paper it is shown that the local discretization error ofs-stage singly-implicit methods of orderp can be estimated by embedding these methods intos-stage two-step Runge-Kutta methods of orderp+1, wherep=s orp=s+1. These error estimates do not require any extra evaluations of the right hand side of the differential equations. This is in contrast with the error estimation schemes based on embedded pairs of two singly-implicit methods proposed by Burrage.The work of A. Bellen and M. Zennaro was supported by the CNR and MPI. The work of Z. Jackiewicz was supported by the CNR and by the NSF under grant DMS-8520900. 相似文献