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Title: A hybrid method for nonlinear least squares that uses quasi-Newton updates applied to an approximation of the Jacobian matrix (English)
Author: Lukšan, Ladislav
Author: Vlček, Jan
Language: English
Journal: Programs and Algorithms of Numerical Mathematics
Volume: Proceedings of Seminar. Hejnice, June 24-29, 2018
Issue: 2018
Year:
Pages: 99-106
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Category: math
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Summary: 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 $A^T f = J^T f$. This property allows us to solve a linear least squares problem, minimizing $\|A d + f\|$ instead of solving the normal equation $A^T A d + J^T f = 0$, where $d \in R^n$ is the required direction vector. Computational experiments confirm the efficiency of the new method. (English)
Keyword: nonlinear least squares
Keyword: hybrid methods
Keyword: trust-region methods
Keyword: quasi-Newton methods
Keyword: numerical algorithms
Keyword: numerical experiments
MSC: 65F30
MSC: 65K10
DOI: 10.21136/panm.2018.11
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Date available: 2019-04-29T13:37:03Z
Last updated: 2021-05-05
Stable URL: http://hdl.handle.net/10338.dmlcz/703066
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