摘要:

A discrete version is developed of the theory [1] of best approximation in the “gauges” sense.

ISSN:0163-0563    

DOI:10.1080/01630569008816381

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

Given a continuous seminorm p on a Hausdorff locally convex space X and nonempty subsets A, B of X, let Proximal(B;A) (resp. Prox(A,B)) denote the set of p-proximal points of B in A (resp. the set of ordered pairs of p-proximal points of the pair (A,B)). In this article we identify suitable familiesA,Bof nonempty subsets of X and natural topologies on them with a view to study continuity properties of B →Proximal( B;A) and (A,B) →Prox(A,B). This leads us to obtain a best approximation result and a coincidence theorem for multifunctions defined on non-compact sets.

ISSN:0163-0563    

DOI:10.1080/01630569008816382

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We analyze the error in finite element methods in approximating, so-called, free or natural convection problems. We also include the effects of conducting solid walls in our analysis. Under a uniqueness condition on the Rayleigh and Prandtl numbers (which we derive), we give direct, quasioptimal error estimates for “div-stable” finite element spaces for the fluid variables and general conforming finite element spaces for the temperature. At larger Rayleigh numbers, we give analogous, asymptotic error estimates, basing this analysis upon local uniqueness properties of the true solution (upT), which we also establish.

ISSN:0163-0563    

DOI:10.1080/01630569008816383

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

The aim of this paper is to give an improvement of a result by Bramble and Hilbert [2] concerning upper bounds for linear functionals on certain Sobolev spaces by showing that the constants in the estimate are independent of the bounded Lipschitz domain Ω.

ISSN:0163-0563    

DOI:10.1080/01630569008816384

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

Moduli of smoothness of Banach space valued functions of a real argument are defined and studied. The classical Whitney's theorem on the error of polynomial approximation [7] is extended to this case. Estimates for quadrature formulae and numerical treatment of abstract differential equations are presented.

ISSN:0163-0563    

DOI:10.1080/01630569008816385

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We find the minimal information cost me(ε) of obtaining an ε–approximation of a linear problem, assuming that available information consists of noisy (perturbed) values I of linear functionals: Perturbations can be absolute or relative, and are assumed to be bounded, each bound dependent on a consecutive number of a functional. We determine the optimal (up to a constant) number of functionals, optimal precisions with which they should be obtained, as well as the best information and algorithm. The results are applied to the problem of recovering functions in s variables withrcontinuous derivatives, where noisy information is given by function values represented in finite precision arithmetic. The minimal cost, measured by the number of binary bits sufficient for representing information from which the εapproximation can be obtained, is then proportional to.

ISSN:0163-0563    

DOI:10.1080/01630569008816386

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

For the solution of linear systems of equations of the formAu=fby iterations, it is customary to consider a splittingA=M−Nwith the iterative process beingandu0is the initial guess. In this paper we extend the theory of Splittings to Banach spaces and in particular we generalize some results by Schneider, Rose and Szyld on splittings and irreducibility ofM-matrices, and those by Schneider, Neumann and Plemmons on the indices ifAandT. We present a new concept of cone-operator irreducibility which generalizes the usual concept of irreducibility. We also introduce the Concept ofG-compatible spittings forM-operators and show its relation to graph compatible Splittings in the finite dimensional case. Most of our results are graph independent.

ISSN:0163-0563    

DOI:10.1080/01630569008816387

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

The present paper shows that compact, non-empty convex sets inRnform a wedge in a well-defined Banach lattice, which turns out to be isometrically Riesz-isomorphic to the continuous functions inSn–1, the unit sphere ofRn. Among other results, we obtain Dini-like convergence results for sets, linking order- and norm-convergence.

ISSN:0163-0563    

DOI:10.1080/01630569008816388

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We develop a calculus structure in the Banach lattice introduced in a preceding paper, having in mind an approximation problem appearing in non-smooth optimization. We show that the essential results depend as much on the order structure as on the analytical one.

ISSN:0163-0563    

DOI:10.1080/01630569008816389

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

In this paper we consider stability and error estimates for nonuniform sampling. There is a large amount of literature on the subject of error estimates for uniform sampling. In this paper we derive estimates by means of operator norms and obtain new bounds for the amplitude error and the time jitter error, which apply for non uniform sampling.

ISSN:0163-0563    

DOI:10.1080/01630569008816390

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor