Cases Where the Newton-Raphson Method FailsDate: 06/30/2005 at 12:25:31 From: Ola Subject: what are the problems with the Newton Raphson method The Newton Raphson method works with certain equations, like f(x) = x^5 - 5x + 3, where a tangent is drawn and it is to find the root of the line between the interval. But it doesn't work on an equation like y = ln(x+1) + 1. When this graph is plotted it does not work, it shows overflow on the Newton Raphson iteration. I find it difficult with the tangent where it converges sometimes and diverges if the initial value is not close to the root, or is near a turning point of y = f(x). Date: 07/01/2005 at 06:58:38 From: Doctor George Subject: Re: what are the problems with the Newton Raphson method Hi Ola, Thanks for writing to Doctor Math. There are different ways in which Newton-Raphson can fail. You already know that Newton-Raphson can fail because of turning points. It can also fail because of asymptotes. In your case I suspect the failure is because your initial estimate is too high compared to the actual solution. This causes your next iteration to evaluate ln(x) at a negative value. ln(x) has an asymptote at zero and is not defined for negative values. Try a lower initial estimate. Does that make sense? Write again if you need more help. - Doctor George, The Math Forum http://mathforum.org/dr.math/ Date: 07/04/2005 at 11:02:37 From: Ola Subject: Thank you (what are the problems with the Newton Raphson method) Thank you very much. It is nice to know that there are people who are willing to help teenagers like myself in mathematics apart from my teacher. |
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