Abstract
In this chapter, we consider the evaluation of a polynomial function of a single variable. We usually compute the value of an arithmetic function by replacing each arithmetic operation by its corresponding floating-point machine operation (see Section 3.5). Roundoff errors and cancellations sometimes cause the calculated result to be drastically wrong. For similar reasons, a naive interval evaluation of a polynomial may lead to intervals so large as to be practically useless. Roundoff and cancellation errors are especially dangerous if we are evaluating a function close to a root, as we will see in Chapter 9 when we compute verified enclosures of zeros of polynomials.
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© 1993 Springer-Verlag Berlin Heidelberg
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Kulisch, U., Hammer, R., Ratz, D., Hocks, M. (1993). Evaluation of Polynomials. In: Numerical Toolbox for Verified Computing I. Springer Series in Computational Mathematics, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78423-1_4
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DOI: https://doi.org/10.1007/978-3-642-78423-1_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-78425-5
Online ISBN: 978-3-642-78423-1
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