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Differentiation

  • Ker-I Ko
Part of the Progress in Theoretical Computer Science book series (PTCS)

Abstract

Computing the derivative of a function is difficult because, intuitively, the derivative depends on the local subtle changes of the function and is hard to compute from the approximation of the function. However, if some nice properties about the function is known (such as the differentiability of the derivative itself) then the derivative may be easy to compute. Formally, we prove that the derivative of a polynomial-time computable function is polynomial-time computable if and only if it has a polynomial modulus of continuity. Conversely, we can construct a function / in P C [0,1] such that its derivative exists everywhere but is not computable.

Keywords

Power Series Bounded Variation Modulus Function Computable Function Absolute Continuity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 1991

Authors and Affiliations

  • Ker-I Ko
    • 1
  1. 1.Department of Computer ScienceState University of New York at Stony BrookStony BrookUSA

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