Civil and Environmental Engineering 2219A/B Lecture Notes - Lecture 22: Secant Method, Approximation Error, Fixed-Point Iteration
12 Mar 2019
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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. Unfortunately, they may diverge as the computation progresses, but when they do converge, they usually do so much faster than bracketing methods. There are 3 open methods that are used for solving roots problems: Very similar to newton-raphson method, but we can use it for the cases that the newton- Raphson method does not work (aka you can"t derive the function or there is no derivative). An open method of approximating roots where the derivative is approximated by a backward finite difference. And subbing the second equation into the first, we yield. Calculate the next estimate of the root from the two initial guesses with. Calculate the absolute relative approximate error | a| using.
