In this chapter we shall study the solution of equations of the form
$${x^p} = N$$
where N is a given number, 0<N< 1, and p is a real number, \({1 \over 2},{1 \over 3}, - 1\), for instance. We shall discuss various sequences x n whose limit is the solution sought and whose terms are defined by recurrence relations, usually of the form
$${x_{n + 1}} = f\left( {{x_n}} \right)$$
where f is a polynomial, or the ratio of two polynomials. We shall be interested mainly in the relative rates of convergence of the sequences. In Chapter 4 we shall discuss the general equation
$$F\left( x \right) = 0$$
and Newton’s Method, discussed there in general terms, provides a single source for the schemes studied in this chapter.


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Copyright information

© Birkhäuser Verlag, Basel 1979

Authors and Affiliations

  • John Todd
    • 1
  1. 1.California Institute of TechnologyUSA

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