A uniformly computable Implicit Function TheoremMathematical Logic Quarterly (2008)
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).
- computable analysis,
- Implicit Function Theorem
Citation InformationTimothy 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/