ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0 Online Edition Research Article
Federica Pes,
Giuseppe Rodriguez
S. 459 - 480 doi:10.1553/etna_vol53s459 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol53s459
Abstract: Nonlinear least-squares problems appear in many real-world applications. When a nonlinear model is used to reproduce the behavior of a physical system, the unknown parameters of the model can be estimated by fitting experimental observations by a least-squares approach. It is common to solve such problems by Newton's method or one of its variants such as the Gauss-Newton algorithm. In this paper, we study the computation of the minimal-norm solution to a nonlinear least-squares problem, as well as the case where the solution minimizes a suitable semi-norm. Since many important applications lead to severely ill-conditioned least-squares problems, we also consider some regularization techniques for their solution. Numerical experiments, both artificial and derived from an application in applied geophysics, illustrate the performance of the different approaches. Keywords: nonlinear least-squares, nonlinear inverse problem, regularization, Gauss-Newton method Published Online: 2020/07/08 06:52:23 Object Identifier: 0xc1aa5576 0x003ba523 Rights: . Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613. …
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |