A doubly relaxed minimal-norm Gauss-Newton method for underdetermined nonlinear least-squares problems
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 computati...
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| creator | Pes, Federica Rodriguez, Giuseppe |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.2101.07560 |
| format | Article |
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| subjects | Computer Science - Numerical Analysis Gauss-Newton method Iterative methods Jacobi matrix method Jacobian matrix Least squares method Mathematics - Numerical Analysis Newton methods Parameter estimation |
| title | A doubly relaxed minimal-norm Gauss-Newton method for underdetermined nonlinear least-squares problems |
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