On Computing Reciprocals of Power Series,

Abstract

Root-finding iterations are used to compute reciprocals of power series. The author shows that Sieveking's algorithm is just Newton iteration applied in the field of power series. Let (L sub n) denote the number of non-scalar multiplications needed to compute the first n+1 terms of the reciprocal. It is shown that n+1 < or = (L sub n) < or = 4n-log (base 2) n. It is conjectured that (L sub n) = 4n - lower order terms. (Modified author abstract)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1973
Accession Number
AD0767702

Entities

People

  • H. T. Kung

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Iterations
  • Mathematical Analysis
  • Mathematics
  • Numerical Analysis
  • Power Series

Fields of Study

  • Mathematics

Readers

  • Linear Algebra