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Polynomials and Series

In: A Graduate Introduction to Numerical Methods

Author

Listed:
  • Robert M. Corless

    (University of Western Ontario, Applied Mathematics)

  • Nicolas Fillion

    (University of Western Ontario, Applied Mathematics)

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. ⊲

Suggested Citation

  • Robert M. Corless & Nicolas Fillion, 2013. "Polynomials and Series," Springer Books, in: A Graduate Introduction to Numerical Methods, edition 127, chapter 0, pages 43-104, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-8453-0_2
    DOI: 10.1007/978-1-4614-8453-0_2
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