Abstract
The paper presents a new rounding error analysis of product and summation algorithms, Horner’s scheme, evaluations of finite continued fractions, computations of determinants of tridiagonal systems, of determinants of second order and a ’fast’ complex multiplication. The error analysis uses the linearization method and new condition numbers constituting optimal bounds in appraisals of the possible errors. The new error estimates are tested by numerous numerical examples.
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© 1980 Springer-Verlag
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Stummel, F. (1980). Rounding Error Analysis of Elementary Numerical Algorithms. In: Alefeld, G., Grigorieff, R.D. (eds) Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis). Computing Supplementum, vol 2. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8577-3_13
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DOI: https://doi.org/10.1007/978-3-7091-8577-3_13
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81566-3
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