Article
A uniformly computable Implicit Function Theorem
Mathematical Logic Quarterly
(2008)
Abstract
We prove uniformly computable versions of the Implicit Function Theorem in its differentiable and non-differentiable forms. We show that the resulting operators are not computable if information about some of the partial derivatives of the implicitly defining function is omitted. Finally, as a corollary, we obtain a uniformly computable Inverse Function Theorem, first proven by M. Ziegler (2006).
Keywords
- Computability,
- computable analysis,
- Implicit Function Theorem
Disciplines
Publication Date
2008
DOI
10.1002/malq.200710040
Publisher Statement
This is the pre-peer reviewed version of the following article: McNicholl, Timothy H. "A uniformly computable implicit function theorem." Mathematical Logic Quarterly 54, no. 3 (2008): 272-279. This article has been published in final form at doi:10.1002/malq.200710040. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving
Copyright 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Citation Information
Timothy H. McNicholl. "A uniformly computable Implicit Function Theorem" Mathematical Logic Quarterly Vol. 54 Iss. 3 (2008) p. 272 - 279 Available at: http://works.bepress.com/timothy-mcnicholl/11/