1. Root-finding

This chapter was last revised on August 29, 2025.

References:

• [Chasnov, 2012] Chapter 2, Root Finding.

• [Sullivan, 2021] Chapter 2, Algebra.

• [Sauer, 2022] Chapter 1, Solving Equations.

• [Burden et al., 2016] Chapter 2, Solutions of Equations of One Variable.

• [Dionne, 2023] Chapter 2, Iterative Methods to Solve Nonlinear Equations.

• [Chenney and Kincaid, 2013] Chapter 3, Nonlinear Equations.

• [Dahlquist and Björck, 2008] Chapter 6, Solving Scalar Nonlinear Equations.

• [Kincaid and Chenney, 1990] Chapter 3, Solutions of Nonlinear Equations, Sections 0 to 4.

• The package SciPy has some functions for this, described in the Scientific Python Lectures [SciPy, 2025] at https://docs.scipy.org/doc/scipy/reference/optimize.html#root-finding. Somewhat surprisingly, root-finding is treated there as a case of optimization.