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.
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References for Chapter 1
Ashenhurst, R. L., Metropolis, N. (1959): Unnormalized floating-point arithmetic. Assoc. Comput. Mach. 6, 415–428.
Bauer, F. L. (1974): Computational graphs and rounding error. SIAM J. Numer. Anal. 11, 87–96.
Bauer, F. L., Heinhold, J., Samelson, K., Sauer, R. (1965): Moderne Rechenanlagen. Stuttgart: Teubner.
Henrici, P. (1963): Error propagation for difference methods. New York:
Wiley. Knuth, D. E. (1969): The Art of Computer Programming. Vol. 2. Seminumerical Algorithms. Reading, Mass.: Addison-Wesley.
Kulisch, U. (1969): Grundzüge der Intervallrechnung. In: D. Laugwitz: Uberblicke Mathematik 2, 51–98. Mannheim: Bibliographisches Institut.
Moore, R. E. (1966): Interval analysis. Englewood Cliffs, N.J.: Prentice-Hall.
Neumann, J. von, Goldstein, H. H. (1947): Numerical inverting of matrices. Bull. Amer. Math. Soc. 53, 1021–1099.
Rademacher, H. A. (1948): 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.
Scarborough, J. B. (1950): Numerical Mathematical Analysis, 2nd edition. Baltimore: Johns Hopkins Press.
Sterbenz, P. H. (1974): Floating Point Computation. Englewood Cliffs, N.J.: Prentice-Hall.
Wilkinson, J.H. (1960): Error analysis of floating-point computation. Numer. Math. 2, 219–340.
Wilkinson, J.H. (1963): Rounding Errors in Algebraic Processes. New York: Wiley.
Wilkinson, J.H. (1965): The Algebraic Eigenvalue Problem. Oxford: Clarendon Press.
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Stoer, J., Bulirsch, R. (2002). Error Analysis. In: Introduction to Numerical Analysis. Texts in Applied Mathematics, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21738-3_1
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DOI: https://doi.org/10.1007/978-0-387-21738-3_1
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