摘要:

We present and test an iterative process, based on a two-grid Newton method,to refine an approximate basis of a maximal invariant subspace associated with a defective eigenvalue of a closed, densely defined, anticompact operator in a Hilbert space. Computations are done with finite element approximations of differential operators.

ISSN:0163-0563    

DOI:10.1080/01630568908816301

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

This paper describes, and analyzes, a method of successive approximations for finding critical points of a function which can be written as the difference of two convex functions. The method is based on using a non-convex duality theory. At each iteration one solves a convex, optimization problem. This alternates between the primal and the dual variables. Under very general structural conditions on the problem, we prove that the resulting sequence is a descent sequence, which converges to a critical point of the problem. To illustrate the method, it is applied to some weighted eigenvalue problems, to a problem from astrophysics, and to some semilinear elliptic equations.

ISSN:0163-0563    

DOI:10.1080/01630568908816302

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630568908816303

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

By the dynamic programming principle the value function of an optimally controlled stochasticswitching process can be shown to satisfy a boundary value problem for a fully nonlinear second-order elliptic differential equation of Hamilton-Jacobi-Bellman (HJB-) type. For the numerical solution of that HJB-equation we present a multi-grid algorithm whose main features arethe use of nonlinear Gauss-Seidel iteration in the smoothing process and an adaptive local choice of prolongations and restrictions in the coarse-to-fine and fine-to-coarse transfers. Local convergence is proved by combining nonlinear multi-grid convergence theory and elementarysubdifferential calculus. The efficiency of the algorithm is demonstrated for optimal advertising in stochastic dynamic sales response models of Vidale-Wolfe type.

ISSN:0163-0563    

DOI:10.1080/01630568908816304

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

Of concern is the degenerate Riccati equation of the form TR+RT=TA+TBR+RTC+RTDR (*). This models a certain transport equation in the half-space. Our first result will concern a unique, positive solution of the operator equation SR+RT=K in a anach space equipped with a cone structure. We then proceed to prove existence of positive solutions for (*) on an L1space of σ-finite measure and a Banach space X, respectively, under different assumptions. Some estimates of the solution with respect to certain norms are obtained.

ISSN:0163-0563    

DOI:10.1080/01630568908816305

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

Maximal regularity results for second order linear parabolic nonhoomogeneous initial-boundary value problems are established. They are used to show existence, uniqueness and C1dependence on the initial value of the solution of general fully nonlinear problems.

ISSN:0163-0563    

DOI:10.1080/01630568908816306

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

Under Kantorovich-type assumptions, a general convergence theorem for inexact Newton methods (i.e., iterative procedures in which the Newton equations are solved approximately) is given. The results cover several situations already considered in the literature.

ISSN:0163-0563    

DOI:10.1080/01630568908816307

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

It is proved that the majority (in the sense of Baire category) of the Lagrange functions of the linear semi-infinite optimization have at most one saddle point. The structure of the set of Lagrange functions for which the saddle point exists is also discussed.

ISSN:0163-0563    

DOI:10.1080/01630568908816308

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

A splitting iteration method is used to approximate the simple bifurcation point and Moore's extended system [14] for the simple bifurcation problems is rewritten here in a symmetric form. The solution paths across the bifurcation point are parametrized in a global structure and traced with a slightly enlarged system, Numerical examples are presented.

ISSN:0163-0563    

DOI:10.1080/01630568908816309

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor

摘要:

We give counterexamples for some statements of Gwinner and make other remarks.

ISSN:0163-0563    

DOI:10.1080/01630568908816310

出版商:Marcel Dekker, Inc.    

年代:1989

数据来源: Taylor