Estimates of the size of the domain of the implicit function theorem: a mapping degree-based approach

In this article, we present explicit estimates of size of the domain on which the implicit function theorem and the inverse function theorem are valid. For maps that are twice continuously differentiable, these estimates depend upon the magnitude of the first-order derivatives evaluated at the point...

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Bibliographic Details
Published in:	Mathematics of control, signals, and systems Vol. 36; no. 1; pp. 139 - 175
Main Authors:	Jindal, Ashutosh, Chatterjee, Debasish, Banavar, Ravi
Format:	Journal Article
Language:	English
Published:	London Springer London 01.03.2024 Springer Nature B.V
Subjects:	Accuracy Communications Engineering Computation Control Control systems Control theory Discrete time systems Domains Electrical networks Estimates Feedback linearization Mapping Mathematics Mathematics and Statistics Mechatronics Networks Numerical analysis Optimization Ordinary differential equations Original Article Power flow Quadratic programming Riccati equation Robotics Robustness (mathematics) Systems Theory Theorems Validity Implicit function theorem Numerical analysis Degree theory Nonlinear analysis
ISSN:	0932-4194, 1435-568X
Online Access:	Get full text
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