Abstract
Assessing the accuracy of the results of calculations is a paramount goal in numerical analysis. One distinguishes several kinds of errors which may limit this accuracy:
-
(1)
errors in the input data,
-
(2)
roundoff errors,
-
(3)
approximation errors.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References for Chapter 1
Ashenhurst, R. L., Metropolis, N.: Unnormalized floating-point arithmetic. J. Assoc. Comput. Mach. 6, 415–428, 1959.
Bauer, F. L.: Computational graphs and rounding error. SIAM J. Numer. Anal. 11, 87–96, 1974.
Heinhold, J., Samelson, K., Sauer, R.: Moderne Rechenanlagen. Stuttgart: Teubner 1965.
Henrici, P.: Error Propagation for Difference Methods. New York: Wiley 1963.
Knuth, D. E.: The Art of Computer Programming. Vol. 2. Seminumerical Algorithms. Reading, Mass.: Addison-Wesley 1969.
Kulisch, U.: Grundzüge der Intervallrechnung. In: D. Laugwitz: Überblicke Mathematik 2, 51–98. Mannheim: Bibliographisches Institut 1969.
Moore, R. E.: Interval Analysis. Englewood Cliffs, N.J.: Prentice-Hall 1966.
Neumann, J. von, Goldstein, H. H.: Numerical inverting of matrices. Bull. Amer. Math. Soc. 53, 1021–1099, 1947.
Rademacher, H. A.: On the accumulation of errors in processes of integration on high-speed calculating machines. Proceedings of a symposium on large-scale digital calculating machinery. Annals Comput. Labor. Harvard Univ. 16, 176–185, 1948.
Scarborough, J. B.: Numerical Mathematical Analysis. Baltimore: Johns Hopkins Press 1930, 2nd edition 1950.
Sterbenz, P. H.: Floating Point Computation. Englewood Cliffs, N.J.: Prentice-Hall 1974.
Wilkinson, J. H.: Error analysis of floating-point computation. Numer. Math. 2, 219–340, 1960.
Wilkinson, J. H.: Rounding Errors in Algebraic Processes. New York: Wiley 1963.
Wilkinson, J. H.: The Algebraic Eigenvalue Problem. Oxford: Clarendon Press 1965.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media New York
About this chapter
Cite this chapter
Stoer, J., Bulirsch, R. (1993). Error Analysis. In: Introduction to Numerical Analysis. Texts in Applied Mathematics, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2272-7_1
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2272-7_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2274-1
Online ISBN: 978-1-4757-2272-7
eBook Packages: Springer Book Archive