Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Step 1
Given . By just seeing the function we can realise that x = 3 is a root of the function with multiplicity 7. (Which means that 3 is a root "7 times!" ).
Now let us consider the Newton's formula for convergence,
We have , (N(x) is the Newton Iteration function)
Hence 3 is a fixed point of N.
Attracting point-Definition
A point x0 is a fixed point of a function f(x) if and only if f(x0) = x0. Such a point x0 is called an attracting fixed point if (With this condition the Newton's iteration steps attracted towards (converges) that fixed point).
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