A doubly relaxed minimal-norm Gauss–Newton method for underdetermined nonlinear least-squares problems
| Autor: | Federica Pes, Giuseppe Rodriguez |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Numerical Analysis
Rank (linear algebra) Underdetermined system Applied Mathematics 65H10 65F22 Numerical Analysis (math.NA) Computational Mathematics Nonlinear system symbols.namesake Non-linear least squares Norm (mathematics) Convergence (routing) Jacobian matrix and determinant FOS: Mathematics symbols Applied mathematics Mathematics - Numerical Analysis Relaxation (approximation) Mathematics |
| Zdroj: | Applied Numerical Mathematics. 171:233-248 |
| ISSN: | 0168-9274 |
| DOI: | 10.1016/j.apnum.2021.09.002 |
| Popis: | When a physical system is modeled by a nonlinear function, the unknown parameters can be estimated by fitting experimental observations by a least-squares approach. Newton's method and its variants are often used to solve problems of this type. In this paper, we are concerned with the computation of the minimal-norm solution of an underdetermined nonlinear least-squares problem. We present a Gauss–Newton type method, which relies on two relaxation parameters to ensure convergence, and which incorporates a procedure to dynamically estimate the two parameters, as well as the rank of the Jacobian matrix, along the iterations. Numerical results are presented. |
| Databáze: | OpenAIRE |
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