Error analysis for polynomial evaluation
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- by A. C. R. Newbery PDF
- Math. Comp. 28 (1974), 789-793 Request permission
Abstract:
A floating-point error analysis is given for the evaluation of a real polynomial at a real argument by Horner’s scheme. A computable error bound is derived. It is observed that when a polynomial has coefficients of constant sign or of strictly alternating sign, one cannot expect better accuracy by reformulating the problem in terms of Chebyshev polynomials.References
- C. W. Clenshaw, A note on the summation of Chebyshev series, Math. Tables Aids Comput. 9 (1955), 118–120. MR 71856, DOI 10.1090/S0025-5718-1955-0071856-0
- F. L. Bauer, Optimally scaled matrices, Numer. Math. 5 (1963), 73–87. MR 159412, DOI 10.1007/BF01385880
- W. M. Gentleman, An error analysis of Goertzel’s (Watt’s) method for computing Fourier coefficients, Comput. J. 12 (1969/70), 160–165. MR 243760, DOI 10.1093/comjnl/12.2.160
- A. C. R. Newbery, Error analysis for Fourier series evaluation, Math. Comp. 27 (1973), 639–644. MR 366072, DOI 10.1090/S0025-5718-1973-0366072-X
- Cornelius Lanczos, Applied analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1956. MR 0084175
- John R. Rice, On the conditioning of polynomial and rational forms, Numer. Math. 7 (1965), 426–435. MR 189283, DOI 10.1007/BF01436257
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp. 28 (1974), 789-793
- MSC: Primary 65D15
- DOI: https://doi.org/10.1090/S0025-5718-1974-0373227-8
- MathSciNet review: 0373227