Newton Raphson Method: Derivation
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hi.
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NUS HIGH!
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Nice very clear
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Thanks agian....another ace on exam in a few hours...u are a great teacher
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How do I find use the tangent to find the initial estimate?
I have a graph of two curves; (y=e^x) and (y=4/x)
And it says I have to find the initial estimate for the root of the equation: x e^x - 4 = 0
The answer is that the solution is the intersection of f(x) - e^x and f(x) = 4/x but that doesn't help me find the actual NUMBER for the initial estimate.
How would I go about finding the initial estimate NUMBER?
xTabbyCat 4 months ago
@xTabbyCat I do not know of a general technique to do so. If the problem is connected to a physical phenomenon, you can use the knowledge of the physical problem to choose a good initial guess. Go to numericalmethods(.)eng(.)usf(.)edu and click on Newton Raphson Method. Click on the textbook chapter to see a physical problem.
numericalmethodsguy 4 months ago
Sir, could you help me with this question?
Use the Newton-Raphson process to determine a value of x near x1 = 0 for which f(x) = 0, where
f(x) = 9 x+0.4−8 sin( x )
giving your answer (and the interim results we ask for) correct to 5 decimal places. What are the values of x and f(x) at the second iteration?
What are the values of x and f(x) at the third iteration?
The value of x (correct to 5 decimal places) such that f(x) = 0.
fullheavy 1 year ago
@fullheavy Just follow the example given in the Newton-Raphson playlist. It is not a difficult problem to do. Be sure that your calculator is set to the radians mode. Once the 5 decimal places do not change in the answer, you have your answer.
numericalmethodsguy 1 year ago
What mean by Es?
MachiP0p0 1 year ago
@MachiP0p0 Es means pre-specified tolerance. It is a stopping criteria to stop iterations. When the absolute relative approximate error is less than pre-specified tolerance, then we can stop the iterations. How do we choose Es? Go to numericalmethods(.)eng(.)usf(.)edu and click on Measuring Errors under Introduction. See pages 5-7 of the pdf file of the texbook chapter.
numericalmethodsguy 1 year ago