Abstract
A model is presented which explains the behavior of the roundoff error in a result quantity when computing precision is varied. A set of hypotheses concerning this a posteriori model is tested in a matrix inversion algorithm. The characteristics of the algorithms where the error model is valid are discussed. As an application of the model, the usual estimation procedure for roundoff error consisting of comparing the results computed in two different precisions is analyzed statistically.
Similar content being viewed by others
References
J. W. Daniel,Correcting approximations to multiple roots of polynomials, Num. Math. 9, 99–102, 1966.
P. Henrici,Discrete variable methods in ordinary differential equations, Wiley, New York, 1962.
P. Henrici,Error propagation for difference methods, Wiley, New York, 1964.
P. Henrici,Elements of numerical analysis, Wiley, New York, 1964.
T. E. Hull and J. R. Swenson,Tests of probabilistic models for propagation of roundoff errors, Comm. ACM, vol. 9, 108–113, 1966.
D. E. Knuth,The art of computer programming, vol. 2, chapter 4, Addison Wesley, New York, 1969.
M. Tienari and V. Suokonautio,A set of procedures making real arithmetic of unlimited accuracy possible within Algol 60, BIT 6, 332–338, 1966.
M. Tienari,Varying length floating point arithmetic: a necessary tool for numerical analyst, Technical report no. CS 62, Computer Science Department, Stanford University, Stanford, California, 1967.
J. Wilkinson,Rounding errors in algebraic processes, Prentice Hall, Englewood Cliffs, N. J., 1963.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tienari, M. A statistical model of roundoff error for varying length floating-point arithmetic. BIT 10, 355–365 (1970). https://doi.org/10.1007/BF01934204
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01934204