Forsythe, George, Michael A. Malcolm, and Cleve B. Moler,
Computer Methods for Mathematical Computations
, Englewood Cliffs, NJ: Prentice-Hall, 1977.
This book describes the computation of
using the Taylor series in Section 2.3.
"What Every Computer Scientist Should Know about Floating-Point Arithmetic,"
ACM Computing Surveys
, Volume 23, Number 1, March 1991.
Higham, Nicolas J.,
Accuracy and Stability of Numerical Algorithms
, Philadelphia: Society for Industrial and Applied Mathematics, 1996.
Implementation of Algorithms, Part I
, Technical Report 20, lecture notes by W.S. Haugeland and D. Hough, Department of Computer Science, University of California, Berkeley, 1973.
Goldberg, Higham, and Kahan describe the Kahan Summation Algorithm. Goldberg contains a detailed analysis and proof of the method. Higham also analyzes the method and describes the even more ingenious
doubly compensated summation
; his Chapter 4 is entirely on summation.
Monahan, John F.,
Numerical Methods of Statistics
, Cambridge, UK: Cambridge University Press, 2001.
This text discusses cancellation errors while computing a sample variance in Section 2.5.