Lecture_09_Newton-Raphson_Method

# Lecture_09_Newton-Raphson_Method - EGR 102 Introduction to...

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1 EGR 102 Lecture 9 1 EGR 102 Introduction to Engineering Modeling Newton-Raphson Method Chapter 6.2 Figures from: “Applied Numerical Methods with MATLAB,” Steven Chapra, McGraw Hill Objectives Know the difference between bracketing and open methods for root location. Learn how to solve a roots problem with the Newton- Raphson method and understand the concept of quadratic convergence. Learn how to use MATLAB’s fzero function to estimate roots. Learn how to manipulate and determine the roots of polynomials with MATLAB. EGR 102 Lecture 9 2

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2 Roots EGR 102 Lecture 9 3 Roots of an equation: Values of x that make ƒ(x) = 0 Also called “zeros” of the equation EGR 102 Lecture 9 4 Nonlinear Equation Solvers Bracketing Bisection Graphical Open Methods Newton-Raphson Iterative Root Solving
3 Open Methods Open methods differ from bracketing methods, in that open methods require only a single starting value or two starting values that do not necessarily bracket a root. may diverge as the computation progresses, but when they do converge, they usually do so much faster than bracketing methods. are based on formulas that require only a single starting value of x or two starting values that do not necessarily bracket the root. EGR 102 Lecture 9 5 Graphical Comparison of Methods a) Bracketing (bisection) method where the root is constrained within the interval bounded by x l and x u b)Diverging open (Newton-Raphson) method where a formula is used to project from x i to x i+1 in an iterative fashion. This method can either (b)

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## This note was uploaded on 04/23/2011 for the course EGR 102 taught by Professor Hinds during the Spring '09 term at Michigan State University.

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Lecture_09_Newton-Raphson_Method - EGR 102 Introduction to...

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