摘要:

This paper establishes a simple and easily-applied criterion for determining whether a multivalued mapping is metrically regular relatively to a subset in the range space.

ISSN:0163-0563    

DOI:10.1080/01630569808816825

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

The controllability of the wave equation with a viscous damping on a bounded interval is considered. The exterior force is taken in the formwithas a control. Necessary and sufficient conditions for exact controllability are established. Such a control brings the oscillating string to rest in a finite time, T. These results are a generalization of the well-known results by D. Russell for an undamped string. The techniques are based on the theory of nonselfadjoint operators in a Hilbert space. Two facts are crucial for this approach. Namely, the set of eigenfunctions of the dynamic generator of the evolution system forms a Riesz basis in the energy space; and the family of nonharmonic exponentials generated by the eigenvalues of the problem forms a Riesz basis in the space. The value of T coincides with the value found by Russell for a continuum without damping.

ISSN:0163-0563    

DOI:10.1080/01630569808816826

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

A general optimal control problem for ordinary differential equations is considered. For this problem, some improvements of the algorithm of Sakawa are discussed. We avoid any convexity assumption and show with an example that the algorithm is even applicable in cases in which no optimal control exists.

ISSN:0163-0563    

DOI:10.1080/01630569808816827

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

It is shown that an approximative property with respect to Orlicz or Luxemburg norms in Orlicz spaces, useful for computing best approximants from some class of functions, is generally satisfied only for the Lp-norms, whenever the measure space contains at least four pairwise disjoint sets of finite and positive measure.

ISSN:0163-0563    

DOI:10.1080/01630569808816828

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

A Kantorovich-type convergence analysis of Ulm's method [15] for solving smooth operator equations in Banach spaces is carried out assuming only regular smoothness of the operator involved instead of the usual Lipschitz smoothness. The theorem proved provides convergence condition, existence and uniqueness radii, a priori and a posteriori error bounds, which are shown to be sharp in the sense of [6]. The method is applied to Chandrasekhar's integral equation arising in radiative transfer.

ISSN:0163-0563    

DOI:10.1080/01630569808816829

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

The ill-posed minimization problems in Hilbert space with quadratic objective function and closed convex constraint set are considered. For the compact set the regularization methods for such problems are well understood [1, 2] The regularizing properties of some Iteration projection methods for noncompact constraint set are the main issues of this paper. We are looking the gradient projection method for the sphere.

ISSN:0163-0563    

DOI:10.1080/01630569808816830

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

This paper deals with the complexity of the Fredholm equationof the second kind with. The problem elements are free term f and belong to the unit ball of [math03]. Available information about the problem consists of evaluations of f and is assumed to be corrupted by uniformly bounded noise. The absolute error in each noisy evaluation is at most δ. First, we give estimation of the n-th optimal radius in the worst case setting. Then, we show that a noisy finite element method with quadrature (FEMQ) has minimal error. Finally, we give the estimate of €complexity of Fredholm problem of the second kind in the worst case setting. To the best of our knowledge, this is the first work on complexity of integral equation with noisy information

ISSN:0163-0563    

DOI:10.1080/01630569808816831

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

A constrained nonlinear problem of computation of values of unbounded operator on the solutions of Initial operator equation is studied. The estimates of the rate of convergence for regularized solutions to (L, g) - minimal solution are obtained if the smoothness conditions are fulfilled. A sufficient conditions of strong convergence of regularized solutions, when we have only a weak approximation of right-hand side of initial equation, are proved.

ISSN:0163-0563    

DOI:10.1080/01630569808816832

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

We study numerical methods for the solution of general linear moment problems, where the solution belongs to a family of nested subspaces of a Hilbert space. Multi-level algorithms, based on the conjugate gradient method and the Landweber-Richardson method are proposed that determine the "optimal" reconstruction level a posteriori from quantities that arise during the numerical calculations. As an important example we discuss the reconstruction of band-limited signals from irregularly spaced noisy samples, when the actual bandwidth of the signal is not available. Numerical examples show the usefulness of the proposed algorithms

ISSN:0163-0563    

DOI:10.1080/01630569808816833

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

In this paper we consider linear ill-posed problemswhere instead of y noisy data yδare available withandis a linear operator between Hilbert spaces X and Y. Assuming the general source conditionwith appropriate functions φ we study following questions:(i) which (best possible) accuracy can be obtained for identifying x fromunder the assumptions(ii) are there special regularization methods which guarantee this best possible accuracy, i.e., which are optimal on the set Mδ,E? Concerning question (i) we prove that under certain conditions there holds inf supwithwhere the ‘inf’ is taken over all methodsand the 'sup' is taken over all.andConcerning question (ii) we prove the optimality of a general class of regularization methods and specify our general optimality results to Tikhonov type methods and to spectral methods. Heat equation problems backward in time which are characterized by different functions φ(λ) serve as model examples.

ISSN:0163-0563    

DOI:10.1080/01630569808816834

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor