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
- Allan Borodin and Ian Munro, The computational complexity of algebraic and numeric problems, Elsevier Computer Science Library: Theory of Computation Series, No. 1, American Elsevier Publishing Co., Inc., New York-London-Amsterdam, 1975. MR 0468309
- 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
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