Exact Formula for Solving a Degenerate System of Quadratic Equations

• Published in: Computational mathematics and mathematical physics Vol. 64; no. 3; pp. 365 - 369
• Main Authors: Evtushenko, Yu. G., Tret’yakov, A. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-03-2024; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Convergence; Degeneration; Formulas (mathematics); General Numerical Methods; Mapping; Mathematical analysis; Mathematics; Mathematics and Statistics; Nonlinear equations; Nonlinear systems; Nonlinearity; Quadratic equations; Quadratic programming; regularity; 2-factor operator; degeneration
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542524030072

The paper is devoted to the solution of a nonlinear system of equations
, where
is a quadratic mapping acting from
to
. The derivative
is assumed to be degenerate at the solution point, which is a major characteristic property of nonlinearity of the mapping. Based on constructions of the
p
-regularity theory, a 2-factor method is proposed for solving the system of equations, which converges at a quadratic rate. Moreover, an exact formula is obtained for solving this quadratic system of equations in the case of a 2-regular mapping
.