Solution of Nonlinear Equations
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.
KeywordsNonlinear Equation Golden Section Extinction Probability Fractional Linear Transformation Incomplete Gamma Function
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- 3.Feller W (1968) An Introduction to Probability Theory and Its Applications, Volume 1, 3rd ed. Wiley, New YorkGoogle Scholar
- 6.Lotka AJ (1931) Population analysis—the extinction of families I. J Wash Acad Sci 21:377–380Google Scholar
- 7.Lotka AJ (1931) Population analysis—the extinction of families II. J Wash Acad Sci 21:453–459Google Scholar
- 8.Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. Cambridge University Press, CambridgeGoogle Scholar