American Mathematical Monthly 114 (7), pp. 588-601.
ISSN/ISBN: 0002-9890 DOI: Not available at this time.
Abstract: Floating-point numbers in computations based on Newton's method are not uniformly distributed, as might be expected, but instead follow a very specific logarithmic distribution known as Benford's law. This fact not only adds a surprising note to a notorious gem of mathematics folklore but also has important implications for the analysis of roundoff errors and, consequently, for estimates of average running times of algorithms. Geometric intuition helps explain why, with hindsight, the emerging of century-old Benford's law from three-century-old Newton's method should not have come as a complete surprise.
Bibtex:
@article {MR2341322,
AUTHOR = {Berger, Arno and Hill, Theodore P.},
TITLE = {Newton's method obeys {B}enford's law},
JOURNAL = {Amer. Math. Monthly},
FJOURNAL = {American Mathematical Monthly},
VOLUME = {114},
YEAR = {2007},
NUMBER = {7},
PAGES = {588--601},
ISSN = {0002-9890},
CODEN = {AMMYAE},
MRCLASS = {65G50 (37N30)},
MRNUMBER = {2341322 (2008h:65016)},
MRREVIEWER = {Uwe Sch{\"a}fer},
}
Reference Type: Journal Article
Subject Area(s): Dynamical Systems, General Interest