A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix

0497192 - ÚI 2020 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
Lukšan, Ladislav - Vlček, Jan
A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix.
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.), s. 99-106. ISBN 978-80-85823-69-1.
[Programs and Algorithms of Numerical Mathematics /19./. Hejnice (CZ), 24.06.2018-29.06.2018]
Institucionální podpora: RVO:67985807
Klíčová slova: nonlinear least squares * hybrid methods * trust-region methods * quasi-Newton methods * numerical algorithms * numerical experiments
Obor OECD: Applied mathematics

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.
Trvalý link: http://hdl.handle.net/11104/0289769