7 Solving Single Algebraic Equations

DOI: 10.1201/9781003256861-7

Chapter Objectives

  • Learn bracketing methods for solving single equations, both bisection and false position.
  • Implement the bracketing methods by developing Python functions.
  • Understand the background behind open methods for solving single equations, including the Newton-Raphson method and the secant method.
  • Develop Python functions to implement the open methods.
  • Learn about a hybrid, bracketing/open method, Brent’s method, and how to use the built-in brentq function from the SciPy optimize module.
  • See how some equations occur naturally in a successive substitution or circular format, x = g(x), and understand the characteristics that govern convergence of fixed-point iteration. ...

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