Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Stable evaluation of polynomials in time $ {\rm log}\,n$

Authors: Roland Kusterer and Manfred Reimer
Journal: Math. Comp. 33 (1979), 1019-1031
MSC: Primary 65G05; Secondary 68C25
MathSciNet review: 528054
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An algorithm is investigated which evaluates real polynomials of degree n in time $ \log n$ at asymptotically minimum costs. The algorithm is considerably stable with respect to round-off.

References [Enhancements On Off] (What's this?)

  • [1] Allan Borodin and Ian Munro, The computational complexity of algebraic and numeric problems, American Elsevier Publishing Co., Inc., New York-London-Amsterdam, 1975. Elsevier Computer Science Library; Theory of Computation Series, No. 1. MR 0468309
  • [2] H. Ehlich and K. Zeller, Auswertung der Normen von Interpolationsoperatoren, Math. Ann. 164 (1966), 105–112 (German). MR 0194799
  • [3] Manfred Reimer, Auswertungsverfahren für Polynome in mehreren Variablen, Numer. Math. 23 (1975), 321–336 (German, with English summary). MR 0381282
  • [4] M. Reimer, Auswertungsalgorithmen fast-optimaler numerischer Stabilität für Polynome, Computing 17 (1976/77), no. 4, 289–296. MR 0431609
  • [5] Theodore J. Rivlin, The Chebyshev polynomials, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Pure and Applied Mathematics. MR 0450850
  • [6] H. S. SHAPIRO, Extremal Problems for Polynomials and Power Series, Master's thesis, M.I.T., Cambridge, Mass., 1951.
  • [7] J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0161456

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65G05, 68C25

Retrieve articles in all journals with MSC: 65G05, 68C25

Additional Information

Keywords: Polynomial evaluation, parallel processing, growth of the error norm
Article copyright: © Copyright 1979 American Mathematical Society