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math.NA2013★ 1 cited
The quantitative Morse theorem
Ta Le Loi, Phan Phien
In this paper, we give a proof of the quantitative Morse theorem stated by {Y. Yomdin} in \cite{Y1}. The proof is based on the quantitative Sard theorem, the quantitative inverse f…
math.NA2012
A numerical approach to some basic theorems in singularity theory
Ta Le Loi, Phan Phien
In this paper, we give the explicit bounds for the data of objects involved in some basic theorems of Singularity theory: the Inverse, Implicit and Rank Theorems for Lipschitz mapp…