Faster Sparse Interpolation of Straight-Line Programs

  • Andrew Arnold
  • Mark Giesbrecht
  • Daniel S. Roche
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8136)

Abstract

We give a new probabilistic algorithm for interpolating a “sparse” polynomial f given by a straight-line program. Our algorithm constructs an approximation f* of f, such that f − f* probably has at most half the number of terms of f, then recurses on the difference f − f*. Our approach builds on previous work by Garg and Schost (2009), and Giesbrecht and Roche (2011), and is asymptotically more efficient in terms of the total cost of the probes required than previous methods, in many cases.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Andrew Arnold
    • 1
  • Mark Giesbrecht
    • 1
  • Daniel S. Roche
    • 2
  1. 1.Cheriton School of Computer ScienceUniversity of WaterlooCanada
  2. 2.United States Naval AcademyUSA

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