Solution method for underdetermined systems of nonlinear equationsстатья
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Аннотация: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.