共查询到20条相似文献,搜索用时 15 毫秒
1.
An algorithm for computing best complex ordinary rational functions is presented. The final step of the procedure consists of solving the system of nonlinear equations defined by the local Kolmogorov criterion before checking recently developed sufficient optimality and uniqueness conditions. Various numerical results are reported exhibiting, in particular, nonunique solutions, saddle points and locally best approximants that are not global. 相似文献
2.
The purpose of this paper is to introduce and to discuss the concept of approximation preserving operators on Banach lattices with a strong unit. We show that every lattice isomorphism is an approximation preserving operator. Also we give a necessary and sufficient condition for uniqueness of the best approximation by closed normal subsets of X+, and show that this condition is characterized by some special operators. 相似文献
3.
Ana C. Matos 《BIT Numerical Mathematics》1991,31(4):686-696
The aim of this paper is to study the acceleration properties of the Cauchy-type approximants defined by Brezinski for periodic-linearly convergent power series. In the case where the sufficient conditions for acceleration are not satisfied, we also propose a new acceleration method for these power series based on those approximants. 相似文献
4.
The paper suggests a new — to the best of the author’s knowledge — characterization of Pareto-optimal decisions for the case of two-dimensional utility space which is not supposed to be convex. The main idea is to use the angle distances between the bisector of the first quadrant and points of utility space. A necessary and sufficient condition for Pareto optimality in the form of an equation is derived. The first-order necessary condition for optimality in the form of a pair of equations is also obtained. 相似文献
5.
Annie Cuyt 《BIT Numerical Mathematics》1986,26(1):71-79
Several definitions of multivariate Padé approximants have been introduced during the last decade. We will here consider all types of definitions based on the choice that the coefficients in numerator and denominator of the multivariate Padé approximant are defined by means of a linear system of equations. In this case a determinant representation for the multivariate Padé approximant exists. We will show that a general recursive algorithm can be formulated to compute a multivariate Padé approximant given by any definition of this type. Here intermediate results in the recursive computation scheme will also be multivariate Padé approximants. Up to now such a recursive computation of multivariate Padé approximants only seemed possible in some special cases. 相似文献
6.
Yu. V. Hnatyuk 《Ukrainian Mathematical Journal》2011,62(12):1879-1895
For the problem of the best uniform approximation of a continuous mapping with compact convex images by sets of other continuous
mappings with compact convex images, we establish necessary and sufficient conditions and a criterion for an element to be
extremal; the criterion obtained is a generalization of the classic Kolmogorov criterion for a polynomial of the best approximation. 相似文献
7.
The aim of this paper is to construct rational approximants for multivariate functions given by their expansion in an orthogonal polynomial system. This will be done by generalizing the concept of multivariate Padé approximation. After defining the multivariate Frobenius–Padé approximants, we will be interested in the two following problems: the first one is to develop recursive algorithms for the computation of the value of a sequence of approximants at a given point. The second one is to compute the coefficients of the numerator and denominator of the approximants by solving a linear system. For some particular cases we will obtain a displacement rank structure for the matrix of the system we have to solve. The case of a Tchebyshev expansion is considered in more detail. 相似文献
8.
Daniel Vera 《Mathematische Nachrichten》2019,292(1):195-210
Restricted non linear approximation is a generalization of the N‐term approximation in which a measure on the index set of the approximants controls the type, instead of the number, of elements in the approximation. Thresholding is a well‐known type of non linear approximation. We relate a generalized upper and lower Temlyakov property with the decreasing rate of the thresholding approximation. This relation is in the form of a characterization through some general discrete Lorentz spaces. Thus, not only we recover some results in the literature but find new ones. As an application of these results, we compress and reduce noise of some images with wavelets and shearlets and show, at least empirically, that the L2‐norm is not necessarily the best norm to measure the approximation error. 相似文献
9.
Let , where B is the open unit ball in (), and let denote the collection of functions h in which are harmonic on B and satisfy on . A function h
* in is called a best harmonic one-sided L
1-approximant to f if for all h in . This paper characterizes such approximants and discusses questions of existence and uniqueness. Corresponding results for
approximation on the cylinder are also established, but the proofs in this case are more difficult and rely on recent work concerning tangential harmonic
approximation. The characterizations are quite different in nature from those recently obtained for harmonic L
1-approximation without a one-sidedness condition.
Received: 25 September 1997 相似文献
10.
B. Hernández-Jiménez M.A. Rojas-Medar R. Osuna-Gómez 《Journal of Mathematical Analysis and Applications》2009,352(2):604-2475
Convexity plays a very important role in optimization for establishing optimality conditions. Different works have shown that the convexity property can be replaced by a weaker notion, the invexity. In particular, for problems with inequality-type constraints, Martin defined a weaker notion of invexity, the Karush-Kuhn-Tucker-invexity (hereafter KKT-invexity), that is both necessary and sufficient to obtain Karush-Kuhn-Tucker-type optimality conditions. It is well known that for this result to hold the problem has to verify a constraint qualification, i.e., it must be regular or non-degenerate. In non-regular problems, the classical optimality conditions are totally inapplicable. Meaningful results were obtained for problems with inequality-type constraints by Izmailov. They are based on the 2-regularity condition of the constraints at a feasible point. In this work, we generalize Martin's result to non-regular problems by defining an analogous concept, the 2-KKT-invexity, and using the characterization of the tangent cone in the 2-regular case and the necessary optimality condition given by Izmailov. 相似文献
11.
《Optimization》2012,61(2):109-123
A linear terminal problem of optimal control with a piecewise-linear terminal constraints is considered. On the base of the concept of a support the optimality criterion is proved and sufficient optimality condition in the form of the maximum principle is formulated. The support enables us to choose from the set of the Lagrange vectors a special one which in the terminology of linear programming is called the basic vector [1]. In the case of nondegeneracy of the support control the sufficient condition under question is proved to be necessary condition 相似文献
12.
Guo-lin Yu 《高校应用数学学报(英文版)》2017,32(2):225-236
There are two approaches of defining the solutions of a set-valued optimization problem:vector criterion and set criterion.This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives.In the case of vector criterion,some optimality conditions are derived for isolated (weak) minimizers.With set criterion,necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation. 相似文献
13.
Giancarlo Bigi 《Mathematical Methods of Operations Research》2006,63(1):77-85
A second order sufficient optimality criterion is presented for a multiobjective problem subject to a constraint given just
as a set. To this aim, we first refine known necessary conditions in such a way that the sufficient ones differ by the replacement
of inequalities by strict inequalities. Furthermore, we show that no relationship holds between this criterion and a sufficient
multipliers rule, when the constraint is described by inequalities and equalities. Finally, improvements of this criterion
for the unconstrained case are presented, stressing the differences with single-objective optimization 相似文献
14.
Cuyt Annie Driver Kathy Tan Jieqing Verdonk Brigitte 《Advances in Computational Mathematics》1999,10(1):29-49
We investigate the approximation of some hypergeometric functions of two variables, namely the Appell functions F
i
, i = 1,...,4, by multivariate Padé approximants. Section 1 reviews the results that exist for the projection of the F
i
onto ϰ=0 or y=0, namely, the Gauss function 2
F
1(a, b; c; z), since a great deal is known about Padé approximants for this hypergeometric series. Section 2 summarizes the definitions
of both homogeneous and general multivariate Padé approximants. In section 3 we prove that the table of homogeneous multivariate
Padé approximants is normal under similar conditions to those that hold in the univariate case. In contrast, in section 4,
theorems are given which indicate that, already for the special case F
1(a, b, b′; c; x; y) with a = b = b′ = 1 and c = 2, there is a high degree of degeneracy in the table of general multivariate Padé approximants. Section 5 presents some concluding
remarks, highlighting the difference between the two types of multivariate Padé approximants in this context and discussing
directions for future work.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
15.
《Optimization》2012,61(5):767-781
This paper consider Markov decision processes with countable state space, compact action spaces and a bounded reward function. Under some recurrence and connectedness condition, including the simultaneous Döblin condition, we prove the existence of bounded solutions of the optimality equations which arise for the multichain case in connection with the average reward criterion and sensitive optimality criteria, and we give a characterization of the sets of n-average optimal decision rules. 相似文献
16.
Peter F. Mah 《Numerical Functional Analysis & Optimization》2013,34(4):311-331
The purpose of this paper is two folded. First, we present some results on strongly Kolmogorov sets, some of which parallel those for Kolmogorov sets. Secondly, we give two conditions which are sufficient for an element of a strongly Kolmogorov set to be a strongly unique best approximation. Then these conditions are shown to be necessary if additional conditions are imposed on either the norm or the set which we approximate from. 相似文献
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19.
集值映射多目标规划的K-T最优性条件 总被引:18,自引:1,他引:17
讨论集值映射多目标规划(VP)的最优性条件问题.首先,在没有锥凹的假设下,利用集值映射的相依导数,得到了(VP)的锥--超有效解要满足的必要条件和充分条件.其次,在锥凹假设和比推广了的Slater规格更弱的条件下,给出了(VP)关于锥--超有效解的K--T型最优性必要条件和充分条件. 相似文献
20.
A criterion for the positivity of a cubic polynomial on a given interval is derived. By means of this result a necessary and sufficient condition is given under which cubicC
1-spline interpolants are nonnegative. Further, since such interpolants are not uniquely determined, for selecting one of them the geometric curvature is minimized. The arising optimization problem is solved numerically via dualization. 相似文献