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

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.

arXiv comment6 pages 1 figure