摘要:

A continuous function f(x,y) is given on the unit square, and it is desired to approximate it in the Tchebycheff sense by a function of the form g(x) + h(y). Several aspects of this problem are studied here. New results are obtained for the Dili-berto-Straus Algorithm, and some examples show how rapidly or how slowly it converges. New estimates are derived for the “degree” of approximation. Further results concern: (1) the description of the set of all best approximations; (2) the special case when f is differentiable; and (3) the least-squares version of the same problem.

ISSN:0163-0563    

DOI:10.1080/01630567908816021

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

摘要:

Convergence of general iteration methods for linear operator equations are investigated in a limit space. If the equation is not solvable, the iterates converge to a generalized solution. If the equation is not uniquely solvable, the initial approximation can be chosen in such a way that the iterates converge to an arbitrary solution. Furthermore, the iteration method yields the inner inverse of the operator. The article generalizes results of G. Mae3 [8] for linear systems of equations with rectangular matrices.

ISSN:0163-0563    

DOI:10.1080/01630567908816022

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

摘要:

This note is first concerned with the approximation of the solution operators for initial-value problems, and that in case the solution operators have a certain smoothing property similar to that of holomorphic semigroups. A convergence theorem with rates given by Peetre-Thomée (and later by Löfström) in the setting of concrete (Besov) spaces is reproduced in the frame of arbitrary Banach spaces. Secondly it is shown that the stable limit laws of probability theory may be seen as an application of this theorem of numerical analysis. Moreover, one obtains sharper rates of convergence for these limit laws.

ISSN:0163-0563    

DOI:10.1080/01630567908816023

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630567908816024

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

摘要:

The solution of the fourth order problembounded in, and its Laplacian are approximated by polynomial finite elements of the same degree,. It is shown that in any subdomainthe approximation toconverges with ‘nearly’ the same order as the approximiation to u does provided u is sufficiently regular.

ISSN:0163-0563    

DOI:10.1080/01630567908816025

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

摘要:

A theorem on differential inequalities related to a simple parabolic free boundary value problem is presented. The result can be used for the construction of pointwise upper and lower bounds of the free boundary curve.

ISSN:0163-0563    

DOI:10.1080/01630567908816026

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

摘要:

Our aim is to investigate the existence of solutions to some second order difference equations of monotone type. Theorems 1.1 and 1.2 below are the discrete versions of some existence results due to V. Barbu [1] corresponding to the continuous case.

ISSN:0163-0563    

DOI:10.1080/01630567908816027

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630567908816020

出版商:Marcel Dekker, Inc.    

年代:1979

数据来源: Taylor