摘要:

Sequences (or curves) are constructed to approximate common fixed points of a pair of nonex-pansive mappings (or contraction semigroups) in Hilbert spaces. The obtained results extend the previously known results from a single mapping to a family of mappings.

ISSN:0163-0563    

DOI:10.1080/01630569808816821

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

Finding an optimal point in the intersection of the fixed point sets of a family of nonexpansive mappings is a frequent problem in various areas of mathematical science and engineering. Letbe nonexpansive mappings on a Hilbert space H, and letbe a quadratic function defined byfor all, whereis a strongly positive bounded self-adjoint linear operator. Then, for each sequence of scalar parameters (λn) satisfying certain conditions, we propose an algorithm that generates a sequence converting strongly to a unique minimizer u*of Θ over the intersection of the fixed point sets of all the Ti’s. This generalizes some results of Halpern (1967), Lions (1977), Wittmann (1992), and Bauschke (1996). In particular, the minimization of Θ over the intersectionof closed convex sets Cican be handled by taking Tito the metric projectiononto Ciwithout introducing any special inner products that depends on A. We also propose an algorithm that generates a sequence converging to a unique minimizer of Θ over, where K is a given closed convex set andfor positive weights. This is applicable to the inconsistent caseas well.

ISSN:0163-0563    

DOI:10.1080/01630569808816822

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

摘要:

A parameter-dependent first-order system arising from elasticity problems is introduced. The system corresponds to the 2D isotropic elasticity equations under a stress-pressure-displacement formulation in which the nonnegative parameter measures the material compressibility for the elastic body. Standard and weighted least squares finite element methods are applied to this system, and analyses for different values of the parameter are performed in a unified manner. The methods offer certain advantages such as they need not satisfy the Babuŝka-Brezzi condition, a single continuous piecewise polynomial space can be used for the approximation of all the unknowns, the resulting algebraic system is symmetric and positive definite, accurate approximations of all the unknowns can be obtained simultaneously, and, especially, computational results do not exhibit any significant numerical locking as the parameter tends to zero which corresponds to the incompressible elasticity problem (or equivalently, the Stokes problem). With suitable boundary conditions, it is shown that both methods achieve optimal rates of convergence in the H1-norm and in the L2-norm for all the unknowns. Numerical experiments with various values of the parameter are given to demonstrate the theoretical estimates.

ISSN:0163-0563    

DOI:10.1080/01630569808816823

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630569808816810

出版商:Marcel Dekker, Inc.    

年代:1998

数据来源: Taylor