Error analysis for polynomial evaluation
Author:
A. C. R. Newbery
Journal:
Math. Comp. 28 (1974), 789793
MSC:
Primary 65D15
MathSciNet review:
0373227
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Abstract: A floatingpoint 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.
 [1]
C. W. Clenshaw, "A note on the summation of Chebyshev series," MTAC, v. 9, 1955, pp. 118120. MR 17, 194. MR 0071856 (17:194e)
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F. L. Bauer, "Optimally scaled matrices," Numer. Math., v. 5, 1963, pp. 7387. MR 28 #2629. MR 0159412 (28:2629)
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W. M. Gentleman, "An error analysis of Goertzel's (Watt's) method for computing Fourier coefficients," Comput. J., v 12, 1969/70, pp. 160165. MR 39 #5081. MR 0243760 (39:5081)
 [4]
A. C. R. Newbery, "Error analysis for Fourier series evaluation," Math. Comp., v. 27, 1973, pp. 639644. MR 0366072 (51:2323)
 [5]
C. Lanczos, Applied Analysis, PrenticeHall, Englewood Cliffs, N. J., 1956. MR 18, 823. MR 0084175 (18:823c)
 [6]
J. R. Rice, "On the conditioning of polynomial and rational forms," Numer. Math., v. 7, 1965, pp. 426435. MR 32 #6710. MR 0189283 (32:6710)
 [1]
 C. W. Clenshaw, "A note on the summation of Chebyshev series," MTAC, v. 9, 1955, pp. 118120. MR 17, 194. MR 0071856 (17:194e)
 [2]
 F. L. Bauer, "Optimally scaled matrices," Numer. Math., v. 5, 1963, pp. 7387. MR 28 #2629. MR 0159412 (28:2629)
 [3]
 W. M. Gentleman, "An error analysis of Goertzel's (Watt's) method for computing Fourier coefficients," Comput. J., v 12, 1969/70, pp. 160165. MR 39 #5081. MR 0243760 (39:5081)
 [4]
 A. C. R. Newbery, "Error analysis for Fourier series evaluation," Math. Comp., v. 27, 1973, pp. 639644. MR 0366072 (51:2323)
 [5]
 C. Lanczos, Applied Analysis, PrenticeHall, Englewood Cliffs, N. J., 1956. MR 18, 823. MR 0084175 (18:823c)
 [6]
 J. R. Rice, "On the conditioning of polynomial and rational forms," Numer. Math., v. 7, 1965, pp. 426435. MR 32 #6710. MR 0189283 (32:6710)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197403732278
PII:
S 00255718(1974)03732278
Keywords:
Error analysis,
polynomials
Article copyright:
© Copyright 1974
American Mathematical Society
