zbMATH — the first resource for mathematics

A numerical approach to \(2k+e\) nonlinear equations with only \(k\) nonlinear variables. (English) Zbl 0754.65045
The author derives a method for solving \(2k+e\) nonlinear algebraic equations in \(2k\) unknowns of the form \(L(x)y-b=0\) with unknowns \(x\) and \(y\), where \(e\) is a positive integer and the entries of the \((2k+e)\times k\) matrix \(L(x)\) are nonlinear functions of \(x\). The method is based on solving a linear overdetermined system and a polynomial equation of the \(k\)-th order. Some numerical tests are also presented.

65H10 Numerical computation of solutions to systems of equations
65F20 Numerical solutions to overdetermined systems, pseudoinverses
Full Text: DOI
[1] Bloomfield, P., Steiger, W. L.: Least absolute deviations. Boston: Birkhäuser 1983. · Zbl 0536.62049
[2] Schapery, R. A.: Approximate methods of transform inversion for viscoelastic stress analysis. Proceedings of the fourth US National Congress of Applied Mechanics, 1075–1085 (1962).
[3] Ypma, T. J., Shen, Q.: SolvingN+m nonlinear equations with onlym nonlinear variables. Computing44, 259–271 (1990). · Zbl 0721.65024 · doi:10.1007/BF02262221
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.