The substitution method we describe consists of expressing the unknown coefficient as a function of data, of the solution to an auxiliary direct problem and of a control parameter. We discuss the connection between this method and equation error minimisation. The equations where the coefficient appears correspond to the following direct problems: (1) the two-point boundary value problem for an ordinary differential equation of elliptic type; (2) its finite-dimensional (discretised) counterpart, where also the domain is discretised; (3) an algebraic equation on a two-dimensional discrete domain, obtained from a Dirichlet boundary value problem. Uniqueness, stability and existence properties are considered. The last case is discussed with reference to a preliminary example, which shows the connection between the identification algorithm and a nonlinear discrete time dynamical system. For reasons of space, only hints for proofs are given.''

Crosta, G. (1987). A Substitution Method Applied to the Identification of the Leading Coefficient Appearing in Linear-Equations of Elliptic Type. In P.C. Sabatier (a cura di), Inverse problems: An interdisciplinary study (pp. 523-532). San Diego : Academic Press Inc JNL-Comp Subscriptions.

A Substitution Method Applied to the Identification of the Leading Coefficient Appearing in Linear-Equations of Elliptic Type

CROSTA, GIOVANNI FRANCO FILIPPO
Primo
1987

Abstract

The substitution method we describe consists of expressing the unknown coefficient as a function of data, of the solution to an auxiliary direct problem and of a control parameter. We discuss the connection between this method and equation error minimisation. The equations where the coefficient appears correspond to the following direct problems: (1) the two-point boundary value problem for an ordinary differential equation of elliptic type; (2) its finite-dimensional (discretised) counterpart, where also the domain is discretised; (3) an algebraic equation on a two-dimensional discrete domain, obtained from a Dirichlet boundary value problem. Uniqueness, stability and existence properties are considered. The last case is discussed with reference to a preliminary example, which shows the connection between the identification algorithm and a nonlinear discrete time dynamical system. For reasons of space, only hints for proofs are given.''
Capitolo o saggio
inverse problems; conductivity identification; two-point boundary value problem; comparison model; equation error; uniqueness conditions
English
Inverse problems: An interdisciplinary study
Sabatier, PC
1987
0-12-014581-2
Academic Press Inc JNL-Comp Subscriptions
523
532
Crosta, G. (1987). A Substitution Method Applied to the Identification of the Leading Coefficient Appearing in Linear-Equations of Elliptic Type. In P.C. Sabatier (a cura di), Inverse problems: An interdisciplinary study (pp. 523-532). San Diego : Academic Press Inc JNL-Comp Subscriptions.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/93769
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