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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Stable evaluation of polynomials in time $\textrm {log} n$
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by Roland Kusterer and Manfred Reimer PDF
Math. Comp. 33 (1979), 1019-1031 Request permission

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
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  • H. Ehlich and K. Zeller, Auswertung der Normen von Interpolationsoperatoren, Math. Ann. 164 (1966), 105–112 (German). MR 194799, DOI 10.1007/BF01429047
  • Manfred Reimer, Auswertungsverfahren für Polynome in mehreren Variablen, Numer. Math. 23 (1975), 321–336 (German, with English summary). MR 381282, DOI 10.1007/BF01438259
  • M. Reimer, Auswertungsalgorithmen fast-optimaler numerischer Stabilität für Polynome, Computing 17 (1976/77), no. 4, 289–296. MR 431609, DOI 10.1007/BF02275642
  • Theodore J. Rivlin, The Chebyshev polynomials, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. MR 0450850
  • H. S. SHAPIRO, Extremal Problems for Polynomials and Power Series, Master’s thesis, M.I.T., Cambridge, Mass., 1951.
  • J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0161456
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Math. Comp. 33 (1979), 1019-1031
  • MSC: Primary 65G05; Secondary 68C25
  • DOI: https://doi.org/10.1090/S0025-5718-1979-0528054-X
  • MathSciNet review: 528054