A mixed least-squares method for an inverse problem of a nonlinear beam equation

Richard E. Ewing; Tao Lin; Yanping Lin

doi:10.1088/0266-5611/15/1/006

A mixed least-squares method for an inverse problem of a nonlinear beam equation

Richard E. Ewing
, Tao Lin
, Yanping Lin

Research output: Journal article publication › Journal article › Academic research › peer-review

8 Citations (Scopus)

Abstract

We discuss a finite-element method based on the mixed least-squares formulation. The cost functional turns out to be a polynomial so that its gradient and Hessian can be computed efficiently. A multi-level Newton iteration is introduced for minimizing the cost functional that can converge from a rough initial guess. Error estimates are derived which not only are optimal in a certain configuration, but also supply rules for choosing regularization parameters according to the mesh size and the random noise in the data.

Original language	English
Pages (from-to)	19-32
Number of pages	14
Journal	Inverse Problems
Volume	15
Issue number	1
DOIs	https://doi.org/10.1088/0266-5611/15/1/006
Publication status	Published - 1 Dec 1999
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Mathematical Physics
Computer Science Applications
Applied Mathematics

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10.1088/0266-5611/15/1/006

Cite this

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AB - We discuss a finite-element method based on the mixed least-squares formulation. The cost functional turns out to be a polynomial so that its gradient and Hessian can be computed efficiently. A multi-level Newton iteration is introduced for minimizing the cost functional that can converge from a rough initial guess. Error estimates are derived which not only are optimal in a certain configuration, but also supply rules for choosing regularization parameters according to the mesh size and the random noise in the data.

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DO - 10.1088/0266-5611/15/1/006

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A mixed least-squares method for an inverse problem of a nonlinear beam equation

Abstract

ASJC Scopus subject areas

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