On Convergence Rates of Root-Seeking Methods
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03-12-2018, 04:13 PM
Post: #38
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RE: On Convergence Rates of Root-Seeking Methods
(03-11-2018 11:36 PM)Paul Dale Wrote: Rather than Newton's which requires the derivative, did you mean secant?I did mean Newton, with a formula to approximate the derivative, or if the expression has a derivative the system can determine it algebraically and use it. (03-11-2018 11:36 PM)Paul Dale Wrote: Dieter is correct, I'd recommend Brent's method for a bracket solver. It is guaranteed to get a solution and is quadratically convergent almost always. There was a modification in the 34S to also include the Ridder's method in addition to Brent's secant, inverse quadratic and bisection methods. Testing indicated that it was beneficial, although I don't remember the conditions under which it is used. Brent seems like a powerhouse combo of other methods. If I implement Brent, does it make any sense to offer the user a choice to use bisection, etc.? It will probably end up being the default method, unless complex mode is enabled, then something like Muller seems to be the only choice? |
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