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Improvements to the cluster Newton method for underdetermined inverse problems
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics. (Pharmacometrics Group)ORCID iD: 0000-0002-5881-2023
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2015 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, Vol. 283, 122-141 p.Article in journal (Refereed) Published
Abstract [en]

The Cluster Newton method (CN method) has proved to be very efficient at finding multiple solutions to underdetermined inverse problems. In the case of pharmacokinetics, underdetermined inverse problems are often given extra constraints to restrain the variety of solutions. In this paper, we propose a new algorithm based on the two parameters of the Beta distribution for finding a family of solutions which best fit the extra constraints. This allows for a much greater control on the variety of solutions that can be obtained with the CN method. In addition, this algorithm facilitates the task of obtaining pharmacologically feasible parameters. Moreover, we also make some improvements to the original CN method including an adaptive margin of error for the perturbation of the target values and the use of an analytical Jacobian in the resolution of the forward problem.

Place, publisher, year, edition, pages
2015. Vol. 283, 122-141 p.
Keyword [en]
Cluster Newton method, Underdetermined inverse problem, Beta distribution, Pharmacokinetics
National Category
Computational Mathematics
Research subject
Mathematics with specialization in Applied Mathematics
URN: urn:nbn:se:uu:diva-244413DOI: 10.1016/j.cam.2015.01.014ISI: 000351645000010OAI: oai:DiVA.org:uu-244413DiVA: diva2:788758
Available from: 2015-02-16 Created: 2015-02-16 Last updated: 2015-04-27Bibliographically approved

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Aoki, Yasunori
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