An Algorithm for Minimax Solution of Overdetermined Systems of Non-linear Equations

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Abstract
The problem of minimizing the maximum residual of a system of non-linear equations is studied in the case where the number of equations is larger than the number of unknowns. It is supposed that the functions defining the problem have continuous first derivatives, and the algorithm is based on successive linear approximations to these functions. The resulting linear systems are solved in the minimax sense, subject to bounds on the solutions, the bounds being adjusted automatically, depending on the goodness of the linear approximations. It is proved that the method always has sure convergence properties. Some numerical examples are given.

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