Title :
A Galerkin-homotopy method for the distributed parameter estimation problem
Author :
Hongsun Fu ; Bo Han
Author_Institution :
Dept. of Math., Dalian Maritime Univ., Dalian, China
fDate :
Oct. 30 2012-Nov. 2 2012
Abstract :
A Galerkin-homotopy method is proposed for the distributed parameter estimation problems of partial differential equations. Based on the Galerkin principle, the problem of inverting the parameter is transformed into the problem of estimating a finite dimensional vector formed by the coefficients of the expansion of the parameter on an orthogonal basis. To overcome the local convergence of traditional iterative methods, the homotopy method is introduced and combined with Tikhonov regularization to form a new and widely convergent method. As a practical application, the distributed parameter estimation problem of an elliptical equation is solved. Numerical results show the method´s effectiveness.
Keywords :
Galerkin method; convergence of numerical methods; elliptic equations; parameter estimation; partial differential equations; vectors; Galerkin-homotopy method; Tikhonov regularization; distributed parameter estimation problem; elliptical equation; finite dimensional vector; local convergence; parameter expansion coefficients; partial differential equations; Approximation methods; Convergence; Equations; Inverse problems; Iterative methods; Mathematical model; Moment methods; Galerkin-homotopy method; Parameter estimation problem; Tikhonov regularization; elliptical equation; ill-posed;
Conference_Titel :
Information and Communication Technologies (WICT), 2012 World Congress on
Conference_Location :
Trivandrum
Print_ISBN :
978-1-4673-4806-5
DOI :
10.1109/WICT.2012.6409227