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Supplementary terminology for nonlinear iterative methods

The purpose of this note is to suggest a supplement to the terminology of [7] and [9] for nonlinear iterative methods for solving F(x) = 0. We feel such a supplement is needed because it is now clear that the so-called <u>quasi-Newton</u> [1], or <u>variable metric</u> [2], or <u>modification</u> [7] methods are here to stay. Furthermore, the current working terminology for these methods is separate, non-standard and not sufficiently suggestive of their proper place in an overview of nonlinear iterative methods. This is borne out by the comments one always encounters when explaining the subject to the uninitiated. One explanation for this dilemma could be that these methods have essentially arrived after the last systematic attempt to standardize nomenclature [7].