In this note, we discuss a generalization of the well-known implicit function theorem to the time-delay case. We show that the latter problem is closely related to the bicausal changes of coordinates ...

This paper is a survey of some results on Newton's method as applied to the implicit function theorem, homotopy methods, and Bezout's theorem. An application to macroeconomics is also described.

Dmitri Goloubentsev, Evgeny Lakshtanov and Vladimir Piterbarg explain in mathematical terms, and demonstrate using a simple example, how the automatic implicit function theorem, a special version of ...

In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a ...

Kreici, P. (1984) Hard Implicit Function Theorem and Small Periodic Solutions to Partial Differential Equations. Commentationes Mathematicae Universitatis Carolinae, 25, 519-536.

This diffeology appears central in numerical methods developped to solve partial differential equations, and we extend the statement of some classical implicit functions theorem by a careful study of ...

A collection of advanced autodiff primitive rules that built upon the implicit function theorem both for discrete problems (like solving linear systems of equations) and (semi-)continuous problems ...

Here, Robinson’s theorem is viewed from the perspective of more recent developments in variational analysis as well as some lesser-known results in the implicit function literature on equations, prior ...