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Cluster Newton Method for Sampling Multiple Solutions of Underdetermined Inverse Problems: Application to a Parameter Identification Problem in Pharmacokinetics
Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada.ORCID iD: 0000-0002-5881-2023
Res Org Informat & Syst, Natl Inst Informat, Chiyoda Ku, Tokyo 1018430, Japan.
Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada.
Tokyo Inst Technol, Midori Ku, Yokohama, Kanagawa 2268503, Japan.
2014 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 36, no 1, B14-B44 p.Article in journal (Refereed) Published
Abstract [en]

A new algorithm is proposed for simultaneously finding multiple solutions of an underdetermined inverse problem. The algorithm was developed for an ODE parameter identification problem in pharmacokinetics for which multiple solutions are of interest. The algorithm proceeds by computing a cluster of solutions simultaneously, and is more efficient than algorithms that compute multiple solutions one-by-one because it fits the Jacobian in a collective way using a least squares approach. It is demonstrated numerically that the algorithm finds accurate solutions that are suitably distributed, guided by a priori information on which part of the solution set is of interest, and that it does so much more efficiently than a baseline Levenberg-Marquardt method that computes solutions one-by-one. It is also demonstrated that the algorithm benefits from improved robustness due to an inherent smoothing provided by the least-squares fitting.

Place, publisher, year, edition, pages
2014. Vol. 36, no 1, B14-B44 p.
Keyword [en]
inverse problems, method of least squares, pharmacokinetics, underdetermined problems
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-244411DOI: 10.1137/120885462ISI: 000333415500016OAI: oai:DiVA.org:uu-244411DiVA: diva2:788753
Available from: 2015-02-16 Created: 2015-02-16 Last updated: 2017-12-04Bibliographically approved

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Aoki, Yasunori

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