I cover these topics (Newton's method and the bisection search) with several examples in this text https://www.amazon.com/dp/B07FL7JR1J It won't be available for free again until 1/15/19, but the software is always free at http://dudleybenton.altervista.org/software/Nonlinear%20Equations/Nonlinear_Equations_examples.zip See the folder examples\bisection An example of using Newton's method to find multiple roots is the abscissas for Gauss Quadrature. I cover that in http://www.amazon.com/dp/B07BS1DN1S, which will be available free after 12/23/18. The software for that is also free at http://dudleybenton.altervista.org/software/Numerical%20Calculus/Numerical_Calculus_examples.zip see the folder xreal and source code gquad.cpp, which uses Newton's method and is implemented with arbitrary precision arithmetic, also included. There are several other examples that just use double precision.

Dudley J Benton

Hello,

Thanks for your kind reply. May you also refer some text/book which is currently available which explains this method/implementation.

Thanks

Numerical Recipes by W.H. Press B.P. Flannery, S.A Teukolsky and W.T. Vetterling?

Henny Schaink

Checked there. Not found.

in Russian: http://prografix.narod.ru/golden.html

Validated Numerics by Warwick Tucker discusses the Interval Newton Method including the automatic bisection (which occurs when there is a root of the derivative inside the interval iterate): https://press.princeton.edu/titles/9488.html

Marcus Webb

Thanks for the reference.