# A comment on the combination of the implicit function theorem and the Morse lemma

arXiv (Cornell University)（2022）

Abstract

The analytic implicit function theorem is extended. The function f of the theorem is integrated with respect to the dependent variable of the implicit function. A geometrical interpretation is given for the sub-geometry of the integral function F by using the Morse lemma. The result is used in the analysis of the hierarchical technique related to the minimization inon-linear parameter identification.

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Key words

implicit function,theorem

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