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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


IMPACT FACTOR increased in 2014: 0.880
Rank 74 out of 310 in category Mathematics and 113 out of 255 in Applied Mathematics in the 2014 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2014: 0.516
Source Normalized Impact per Paper (SNIP) 2014: 1.430
Impact per Publication (IPP) 2014: 0.613

Mathematical Citation Quotient (MCQ) 2014: 0.51

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A sensitivity matrix based methodology for inverse problem formulation

A. Cintrón-Arias1 / H. T. Banks2 / A. Capaldi3 / A. L. Lloyd4

1Center for Research in Scientific Computation & Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695, USA. Email:

2Center for Research in Scientific Computation & Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695, USA. Email:

3Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695, USA. Email:

4Center for Research in Scientific Computation & Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695, USA. Email:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 17, Issue 6, Pages 545–564, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2009.034, August 2009

Publication History

Received:
2009-04-10
Published Online:
2009-08-19

Abstract

We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects in a score for a vector parameter defined using the norm of the vector of standard errors for components of estimates divided by the estimates. In some cases the method leads to reduction of the standard error for a parameter to less than 1% of the estimate.

Key words.: Inverse problems; ordinary least squares; sensitivity matrix; Fisher Information matrix; parameter selection; standard errors

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