摘要:

This paper considers techniques for obtaining strict error bounds to the back-and-forth shooting method for two-point boundary-value problems. Special attention is paid to the practical computation of certain constants, from which the existence of a true solution in the vicinity of the computed one may be concluded. These techniques can be used in proving the existence of solutions, as is shown in an example.

ISSN:0163-0563    

DOI:10.1080/01630568708816223

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

This paper describes a possibility for approximate solution of stochastic programming problems with complete recourse. We replace the static form of linear problem in Lp-space by a sequence of discretized problems in finite-dimensional spaces. We present conditions that guarantee the convergence of optimal values of discretized problems to the optimal value of the initial problem.

ISSN:0163-0563    

DOI:10.1080/01630568708816224

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

Interval analysis is applied to the fixed-point problem x=ϕ(x) for continuous ϕ:S→S, where the space S is constructed from Cartesian products of the set R of real numbers, with componentwise definitions of arithmetic operations, ordering, and the product topology. With the aid of an interval inclusion φ:IS → IS in the interval space IS corresponding to S, interval iteration is used to establish the existence or nonexistence of a fixed point x*of ϕ in the initial interval X0. Each step of the interval iteration provides lower and upper bounds for fixed points of ϕ in the initial interval, from which approximate values and guaranteed error bounds can be obtained directly. In addition to interval iteration, operator equation and dissection methods are considered briefly.

ISSN:0163-0563    

DOI:10.1080/01630568708816225

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

In this paper, we considerably extend our earlier result about convergence in distribution of approximate solutions: of random operator equations, where the stochastic inputs and the underlying deterministic equation are simultaneously approximated. As a by-product, we obtain convergence results for approximate solutions of equations between spaces of probability measures. We apply our results to random Fredholm integral equations of the second kind and to a random [nbar]onlinear elliptic boundary value problem.

ISSN:0163-0563    

DOI:10.1080/01630568708816226

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

We obtain several theoretical results concerning functions defined from an increasing family of subsets of Rndepending on a real parameter and the level sets of an arbitrary function. These results are applied to the study of the minimal time function of a control process described by a linear differential system, under different assumptions on the control restraint set.

ISSN:0163-0563    

DOI:10.1080/01630568708816227

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

The purpose of this paper is to study the problem of existence of subspaces G of C(X) whereis a compact disconnected subset of the real line or a compact subset ofsuch that G guarantees uniqueness of best L1-approximations for weighted approximation of continuous real-valued functions. Some examples of such subspaces, including subspaces of polynomials and linear spline functions of two variables, are presented.

ISSN:0163-0563    

DOI:10.1080/01630568708816228

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

The main purpose of this paper is to give a proof of quantitative resonance and condensation principles via Baire category arguments in contrast to the gliding hump method used previously. Thereby a new nonquantitative resonance principle is established which is concerned with dominated convergence in Frechet spaces, by the way yielding more detailed information on the structure of the underlying spaces. On the other hand, Baire's approach is an easy tool to develop condensation principles by considering residual sets. Finally, some typical applications concerning trigonometric Fourier partial sums may illustrate the result received.

ISSN:0163-0563    

DOI:10.1080/01630568708816229

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

Sufficient and necessary optimality conditions are given for weakly minimized optimization problems in terms of a vector valued Lagrangian. Lagrangian and Wolfe type duals are constructed and duality established using an ordering that accords with the definition of a weak minimum. The results for differentiable problems continue to hold under weakened convexity assumptions and for problems which quasiminimize rather than minimize.

ISSN:0163-0563    

DOI:10.1080/01630568708816230

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

摘要:

In this paper non-negative solutions of a system of m linear equations. A x = b, in n unknowns which minimize the residual error when Rmis equipped with a strictly convex norm are sought. An implementable iterative algorithm accomplishing this is given. As a special case, we test this for the lp-norms (1 < p < ∞). Each iteration cycle involves the solution of a non-negative least squares problem with a suitably modified right hand side. After presenting certain duality theorems the optimal solutions of the problem are characterized. Convergence of the algorithm is then proved. Numerical results are also included.

ISSN:0163-0563    

DOI:10.1080/01630568708816231

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630568708816222

出版商:Marcel Dekker, Inc.    

年代:1987

数据来源: Taylor