Lower Bounds on the Continuation of Holomorphic Functions

Authors:
Robert Rettinger
Affiliations:
Lehrgebiet Algorithmen und Komplexität, FernUniversität Hagen, D-58084 Hagen, Germany
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2008

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Abstract

We show that continuation of holomorphic functions needs time at least @W(n^2) in the uniform case, which is optimal up to a polylogarithmic factor. In the non-uniform case, i.e. assuming f to be computable in time O(t) on an open subset of its domain, we show, that continuation of f cannot be robustly done in time o(n@?t(n)). This again is optimal up to a polylogarithmic factor.