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A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix
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SYSNO ASEP 0497192 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix Author(s) Lukšan, Ladislav (UIVT-O) SAI, RID
Vlček, Jan (UIVT-O) SAI, RID, ORCIDSource Title Programs and Algorithms of Numerical Mathematics 19. - Prague : Institute of Mathematics of the Czech Academy of Sciences, 2019 / Chleboun J. ; Kůs P. ; Přikryl P. ; Rozložník M. ; Segeth K. ; Šístek J. ; Vejchodský T. - ISBN 978-80-85823-69-1 Pages s. 99-106 Number of pages 8 s. Publication form Online - E Action Programs and Algorithms of Numerical Mathematics /19./ Event date 24.06.2018 - 29.06.2018 VEvent location Hejnice Country CZ - Czech Republic Event type WRD Language eng - English Country CZ - Czech Republic Keywords nonlinear least squares ; hybrid methods ; trust-region methods ; quasi-Newton methods ; numerical algorithms ; numerical experiments Subject RIV BA - General Mathematics OECD category Applied mathematics Institutional support UIVT-O - RVO:67985807 UT WOS 000576737400011 DOI 10.21136/panm.2018.11 Annotation In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation A of the Jacobian matrix J, such that AT f = JT f. This property allows us to solve a linear least squares problem, minimizing ∥Ad+f∥ instead of solving the normal equation ATAd+JT f = 0, where d ∈ Rn is the required direction vector. Computational experiments confirm the efficiency of the new method. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2020
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