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.: 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.
Bauer, F. L., 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.
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Stoer, J., Bulirsch, R. (1980). Error Analysis. In: Introduction to Numerical Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5592-3_1
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DOI: https://doi.org/10.1007/978-1-4757-5592-3_1
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