Civil and Environmental Engineering 2219A/B Lecture Notes - Lecture 21: Secant Method, Approximation Error, Horse Length

• School: Western University
• Department: Civil and Environmental Engineering
• Course: Civil and Environmental Engineering 2219A/B
• Professor: Martha Dagnew

Document Summary

Differ from bracketing methods, in that open methods require only a single starting or two starting values that do not necessarily bracket the root. Unfortunately may diverge as the computation progresses, but when they do converge, they usually do so much faster than bracketing methods. Converge = method yields a result which approaches to the solution. Diverges = method yields a result which is going away from the solution. There are 3 open methods that are used for solving roots problems: This method employs the derivative (slope) of a function to estimate its intercept with the axis of the independent variable. A tangent to the function of (i. e. ( )) is extrapolated down to the x axis to provide an estimate of the root at +1. Use an initial guess of the root to estimate the new value of the root, +1, as: Calculate the absolute relative approximate error, | |