摘要:

In this paper we obtain a solution to the long-standing question of what is a minimal projection fromC[—1,1] onto the quadratics. A recently developed general theory characterizing minimal projections (see [2]) is used both for obtaining the form of the minimal projection and for determining the values of the parameters appearing in the form.

ISSN:0163-0563    

DOI:10.1080/01630569008816357

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We describe the behaviour under interpolation of a limit class of approximation spaces. We characterize them as extrapolation spaces. Moreover, we study the boundedness of certain operators on these spaces. As an application, we derive several results on Macaev operator ideals.

ISSN:0163-0563    

DOI:10.1080/01630569008816358

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

In the eighteenth century, Landen, Lagrange and Gauss studied a function of two positive real numbers that has become known as the arithmetic-geometric mean (AGM). In the nineteenth century, Borchardt generalized the AGM to a function of any 2n(n = 1,2,3,…) positive real numbers. In this paper, we generalize the AGM to a function of any even number of positive real numbers. If M(a, b) is the original AGM then M(a, b) is concave in the pair (a, b) of positive numbers and log M(eα, eβ) is convex in the pair (α,β) of real numbers; all our generalizations of the AGM behave similarly. We generalize this analysis extensively.

ISSN:0163-0563    

DOI:10.1080/01630569008816359

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

For a constrained multicriteria optimization problem with differentiable functions, but not assuming any convexity, vector analogs of quasimin, Kuhn-Tucker point, and (suitably defined) vector quasisaddlepoint are shown to be equivalent. A constraint qualification is assumed. Similarly, a proper (by Geoffrion's definition) weak minimum is equivalent to a Kuhn–Tucker point with a strictly positive multiplier for the objective, and also to a vector quasisaddlepoint with an attached stability property. Under generalized invex hypotheses, these properties reduce to proper minimum and stable saddlepoint. Various known results are thus unified.

ISSN:0163-0563    

DOI:10.1080/01630569008816360

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

In this paper we present a constructive strategy for one-sided approximation of multivariate functions of bounded variation. The approach is based on a special kind of Lebesgue-Stieltjes convolution operator depending on a hyperbolic argument. We prove local, global, and saturation-type results and, finally, take a look at the applicability of the new operators.

ISSN:0163-0563    

DOI:10.1080/01630569008816361

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

In this paper we consider non-linear ill-posed problemsF(x)=y0 in a Hilbert space setting. We solve these problems with Tikhonov regularization combined with finite-dimensional approximation where the datay0 and the non-linear operatorFare assumed to be known only approximately. Conditions are given that guarantee optimal convergence rates with respect to both, the data noise and the finite-dimensional approximation. Finally, we present some numerical results for parameter estimation problems that verify the theoretical results.

ISSN:0163-0563    

DOI:10.1080/01630569008816362

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

In this paper we use fixed point and coincidence theorems due to Park [8] to give matching theorems concerning closed coverings of nonempty convex sets in a real topological vector space. Our new results extend previously given ones due to Ky Fan [2], [3], Shih [10], Shih and Tan [11], and Park [7].

ISSN:0163-0563    

DOI:10.1080/01630569008816363

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We consider a linear ill-posed operator equationAx = yin Hilbert spaces. An algorithmRε:Y→Xfor solving this equation with given inexact right-hand sideyε, such that, is called order optimal if it provides best possible error estimates under the assumption that the minimal norm solutionx*of this operator equation fulfils some smoothness condition. It is shown that if such an algorithm is slightly modified tothen it is a regularization method, i.e., we havewithout additional conditions onx*.

ISSN:0163-0563    

DOI:10.1080/01630569008816364

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

The paper deals with regularization methods for solving ill posed problems with nonselfadjoint bounded linear operators acting on a Hilbert space. A class of methods generated by certain families of functions is considered. In the case of exact data the convergence of approximate solutions to the exact one (provided that it exists) is proved and error estimations are presented. An integral representation of functions of an auxiliary operator is obtained and subsequently used in error estimation.

ISSN:0163-0563    

DOI:10.1080/01630569008816365

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

In a well-known paper [8], J. Schröder studied the method of successive iteration by means of a generalised distance concept. The aim of thise note is to show that in important cases the theorem of J. Schröder can be reformulated as a statement on the convergence of the method of successive approximation in a Banach space with respect to an appropriate norm.

ISSN:0163-0563    

DOI:10.1080/01630569008816366

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor