Polynomials and Series

Robert M. Corless and Nicolas Fillion
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Robert M. Corless: University of Western Ontario, Applied Mathematics
Nicolas Fillion: University of Western Ontario, Applied Mathematics

Chapter Chapter 2 in A Graduate Introduction to Numerical Methods, 2013, pp 43-104 from Springer

Abstract: Abstract This chapter introduces the reader to the numerical aspects of polynomials. In particular, we examine different polynomial bases such as the monomial, the Chebyshev, and the Lagrange basis; we provide algorithms to evaluate polynomials in many of those bases and examine the different condition numbers in different bases. We give a first look at the important problem of numerically finding zeros and pseudozeros of polynomials. We give an algorithmic overview of the numerical computation of truncated power series including Taylor series. Finally, we give a brief discussion of asymptotics. ⊲

Keywords: Condition Number; Orthogonal Polynomial; Chebyshev Polynomial; Polynomial Basis; Gauge Function (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-8453-0_2

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DOI: 10.1007/978-1-4614-8453-0_2

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