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Acta Informatica

, Volume 3, Issue 2, pp 123–133 | Cite as

A unified view of the complexity of evaluation and interpolation

  • Ellis Horowitz
Article
  • 30 Downloads

Summary

Four problems are considered: 1) from an n-precision integer compute its residues modulo n single precision primes; 2) from an n-degree polynomial compute its values at n points; 3) from n residues compute the unique n-precision integer congruent to the residues; 4) from n points compute the unique interpolating polynomial through those points. If M (n) is the time for n-precision integer multiplication, then the time for problems 1 and 2 is shown to be M (n) log n and for problems 3 and 4 to be M (n) (log n) 2. Moreover it is shown that each of the four algorithms are really all instances of the same general algorithm. Finally it is shown how preconditioning or a change of domain will reduce the time for problems 3 and 4 to M (n) (log n).

Keywords

Information System Operating System Data Structure Communication Network Information Theory 
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

© Springer-Verlag 1974

Authors and Affiliations

  • Ellis Horowitz
    • 1
  1. 1.Computer Science Program University of Southern California Powell HallLos AngelesUSA

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