Abstract
Solving linear and nonlinear equations is a major preoccupation of applied mathematics and statistics. For nonlinear equations, closed-form solutions are the exception rather than the rule. Here we will concentrate on three simple techniques—bisection, functional iteration, and Newton’s method— for solving equations in one variable. Insight into how these methods operate can be gained by a combination of theory and examples. Since functional iteration and Newton’s method generalize to higher-dimensional problems, it is particularly important to develop intuition about their strengths and weaknesses. Equipped with this intuition, we can tackle harder problems with more confidence and understanding.
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Lange, K. (2010). Solution of Nonlinear Equations. In: Numerical Analysis for Statisticians. Statistics and Computing. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5945-4_5
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DOI: https://doi.org/10.1007/978-1-4419-5945-4_5
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