Automatically assigned DDC number: 515353

Manually assigned DDC number: 515353

Number of references: 16

Title: Preconditioned All-At-Once Methods for Large, Sparse Parameter Estimation Problems

Author:

Author:

Subject: E. Haber,U. M. Ascher Preconditioned All-At-Once Methods for Large, Sparse Parameter Estimation Problems

Description: The problem of recovering a parameter function based on measurements of solutions of a system of partial differential equations in several space variables leads to a number of computational challenges. Upon discretization of a regularized formulation a large, sparse constrained optimization problem is obtained. Typically in the literature, the constraints are eliminated and the resulting unconstrained formulation is solved by some variant of Newton's method, usually the Gauss-Newton method. A preconditioned conjugate gradient algorithm is applied at each iteration for the resulting reduced Hessian system. In this paper we apply instead a preconditioned Krylov method directly to the KKT system arising from a Newton-type method for the constrained formulation (an "all-at-once" approach). A variant of symmetric QMR is employed, and an effective preconditioner is obtained by solving the reduced Hessian system approximately. Since the reduced Hessian system presents significa...

Contributor: The Pennsylvania State University CiteSeer Archives

Publisher: unknown

Date: 2000-12-29

Pubyear: 2000

Format: ps

Identifier: http://citeseer.ist.psu.edu/386068.html

Source: http://www.cs.ubc.ca/spider/ascher/papers/ha1.ps.gz

Language: en

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