Solution method for underdetermined systems of nonlinear equations
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Ewa Szczepanik
Abstract
In this paper we present a new solution method for underdetermined systems of nonlinear equations in a neighborhood of a certain point of the variety of solutions where the Jacoby matrix has incomplete rank. Such systems are usually called degenerate. It is known that the Gauss–Newton method can be used in the degenerate case. However, the variety of solutions in a neighborhood of the considered point can have several branches in the degenerate case. Therefore, the analysis of convergence of the method requires special techniques based on the constructions of the theory of p-regularity and p-factor-operators.
Funding: The work was supported by the Russian Science Foundation grant 19–11–00338.
References
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Articles in the same Issue
- Frontmatter
- Efficient projection method for a system of differential equations of Fokker−Planck type
- Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation
- Subgrid modelling of convective diffusion in a multiscale random medium
- Solution method for underdetermined systems of nonlinear equations
- Boundary least squares method with three-dimensional harmonic basis of higher order for solving linear div-curl systems with Dirichlet conditions
Articles in the same Issue
- Frontmatter
- Efficient projection method for a system of differential equations of Fokker−Planck type
- Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation
- Subgrid modelling of convective diffusion in a multiscale random medium
- Solution method for underdetermined systems of nonlinear equations
- Boundary least squares method with three-dimensional harmonic basis of higher order for solving linear div-curl systems with Dirichlet conditions
