摘要:

The paper deals with the Backus-Gilbert or averaging kernel inversion of linear integral equations. The theoretical background of the method is developed: it is shown that the method leads to a sequence of linear pointwise estimates, which are asymptotically unbiased when no error is present. Anumerical implementation is given. Finally, the algorithm is applied to numerical differentiation, Laplace transform inversion and to a geophysical inverseproblem arising in electromagnetic sounding.

ISSN:0163-0563    

DOI:10.1080/01630568708816267

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

This paper deals with the optimal solution of ill-posed linear problems, i.e..linear problems for which the solution operator is unbounded. We consider worst-case ar,and averagecase settings. Our main result is that algorithms having finite error (for a given setting) exist if and only if the solution operator is bounded (in that setting). In the worst-case setting, this means that there is no algorithm for solving ill-posed problems having finite error. In the average-case setting, this means that algorithms having finite error exist if and only lf the solution operator is bounded on the average. If the solution operator is bounded on the average, we find average-case optimal information of cardinality n and optimal algorithms using this information, and show that the average error of these algorithms tends to zero as n→∞. These results are then used to determine the €-complexity, i.e., the minimal costof finding an €-accurate approximation. In the worst-case setting, the €comp1exity of an illposed problem is infinite for all €>0; that is, we cannot find an approximation having finite error and finite cost. In the average-case setting, the €-complexity of an ill-posed problem is infinite for all €>0 iff the solution operator is not bounded on the average, moreover, if the the solutionoperator is bounded on the average, then the €-complexity is finite for all €>0.

ISSN:0163-0563    

DOI:10.1080/01630568708816268

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630568708816269

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

An a posteriori error bound for the Zincenko iteration for solving nonlinear equations in Banach spaces is given without proff in Zabrejko and Nguen [7]. In the present paper, this bound is dervied based on a principle developed in a series of papers by Yamamoto[4-6]. Furthermore, it is shown to be sharper than Miel-type bounds[2]

ISSN:0163-0563    

DOI:10.1080/01630568708816270

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

Optimal switching for a nonlinear evolution equation is considered. A type of approximating problems with value functions {uu0<u<u0} is studied. We prove that each uuis the unique viscositY solution of corresponding Hami1ton-Jacoby system, uuconvergesto the value function u of the original problem as µ goes to 0, and an optimal control is determined.

ISSN:0163-0563    

DOI:10.1080/01630568708816271

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

Let (Ω,F,m) be a finite measure space and β be a sub-o-algebra of F. It x is a Banach space, we let L1ΩF,X, L1β,X denote the space of F-measurable (β-measurable) Bochner integrable functions with respect to. It is proved that if x is reflexive and Ω,β,m is separable, than L1,Ω,β,x is proximinal in L1,F,X.

ISSN:0163-0563    

DOI:10.1080/01630568708816272

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

In this paper we obtain approximate solvability results for hammerstein operator equation using the idea of asymptotic compactness and theory of monotone operators.

ISSN:0163-0563    

DOI:10.1080/01630568708816273

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630568708816274

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

We study the maximal branch of solutions for a bifurcation phenomena in variational inequalities. We give optimal results in L∞norm for the approximation by finite element method and sharp estimates for the localization of the continuous and discreate free boundary as the bifurcation parameter goes to infinity. We also obtain lipchitz regularity results for the maximal branch. We establish in some cases a stability condition which has appeared of great importance in the description of the bifurcation phenomena and in the numerical analysis study.

ISSN:0163-0563    

DOI:10.1080/01630568708816275

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630568708816266

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor