Abstract
There are many elementary functions that play important roles in mathematics, and whose properties have long been well known. Some of these are important also in the construction of numerical methods, and they occur in two different roles. One role is as part of the numerical algorithms where certain solutions are represented in terms of these functions for easy evaluation. The other role is as a tool for analysis of the algorithms. In this case the functions are not used as part of the computational algorithm, but they are used in order to understand the fundamental properties of it.
In this chapter we shall concentrate on the three most frequently used types of functions, which are polynomials, trigonometric functions and the exponential function. Most of the material is elementary, but the parts about nonstandard polynomials and about the exponential function with complex arguments are more advanced.
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© 2011 Springer-Verlag Berlin Heidelberg
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Gustafsson, B. (2011). Elementary Functions. In: Fundamentals of Scientific Computing. Texts in Computational Science and Engineering, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19495-5_5
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DOI: https://doi.org/10.1007/978-3-642-19495-5_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19494-8
Online ISBN: 978-3-642-19495-5
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