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Operator Equation (operator + equation)
Selected AbstractsLandweber scheme for compact operator equation in Hilbert space and its applicationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2009Gangrong Qu Abstract We study the Landweber scheme for linear compact operator equation in infinite Hilbert spaces. Using the singular value decomposition for compact operators, we obtain a formula for the Landweber scheme after n iterations and iterative truncated error and consequently establish its convergence conditions. Our results extend known results on convergence conditions. As applications, we apply the Landweber scheme to the X-ray tomography and extrapolation of band-limited functions, and establish accelerated strategies for each application. Copyright © 2008 John Wiley & Sons, Ltd. [source] On the a priori and a posteriori error analysis of a two-fold saddle-point approach for nonlinear incompressible elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2006Gabriel N. Gatica Abstract In this paper, we reconsider the a priori and a posteriori error analysis of a new mixed finite element method for nonlinear incompressible elasticity with mixed boundary conditions. The approach, being based only on the fact that the resulting variational formulation becomes a two-fold saddle-point operator equation, simplifies the analysis and improves the results provided recently in a previous work. Thus, a well-known generalization of the classical Babu,ka,Brezzi theory is applied to show the well-posedness of the continuous and discrete formulations, and to derive the corresponding a priori error estimate. In particular, enriched PEERS subspaces are required for the solvability and stability of the associated Galerkin scheme. In addition, we use the Ritz projection operator to obtain a new reliable and quasi-efficient a posteriori error estimate. Finally, several numerical results illustrating the good performance of the associated adaptive algorithm are presented. Copyright © 2006 John Wiley & Sons, Ltd. [source] Shape reconstruction of an inverse boundary value problem of two-dimensional Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2010Wenjing Yan Abstract This paper is concerned with the problem of the shape reconstruction of two-dimensional flows governed by the Navier,Stokes equations. Our objective is to derive a regularized Gauss,Newton method using the corresponding operator equation in which the unknown is the geometric domain. The theoretical foundation for the Gauss,Newton method is given by establishing the differentiability of the initial boundary value problem with respect to the boundary curve in the sense of a domain derivative. The numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible. Copyright © 2009 John Wiley & Sons, Ltd. [source] A complete boundary integral formulation for compressible Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2005Yang ZuoshengArticle first published online: 29 DEC 200 Abstract A complete boundary integral formulation for compressible Navier,Stokes equations with time discretization by operator splitting is developed using the fundamental solutions of the Helmholtz operator equation with different order. The numerical results for wall pressure and wall skin friction of two-dimensional compressible laminar viscous flow around airfoils are in good agreement with field numerical methods. Copyright © 2004 John Wiley & Sons, Ltd. [source] Computability of solutions of operator equationsMLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 4-5 2007Volker Bosserhoff Abstract We study operator equations within the Turing machine based framework for computability in analysis. Is there an algorithm that maps pairs (T, u) (where T is given in form of a program) to solutions of Tx = u ? Here we consider the case when T is a bounded linear mapping between Hilbert spaces. We are in particular interested in computing the generalized inverse T,u, which is the standard concept of solution in the theory of inverse problems. Typically, T, is discontinuous (i. e. the equation Tx = u is ill-posed) and hence no computable mapping. However, we will use effective versions of theorems from the theory of regularization to show that the mapping (T, T *, u, ,T,u ,) , T,u is computable. We then go on to study the computability of average-case solutions with respect to Gaussian measures which have been considered in information based complexity. Here, T, is considered as an element of an L2 -space. We define suitable representations for such spaces and use the results from the first part of the paper to show that (T, T *, ,T,,) , T, is computable. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||