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  3. formulate newton’s method for the system x^3 = y

Formulate Newton’s method for the system x^3 = y y^3 = x Note that this system has three...

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Advance Math

Formulate Newton’s method for the system
x^3 = y

y^3 = x

Note that this system has three real roots (?1, ?1), (0, 0) and(1, 1). By taking various initial points in the square ?2 < x, y< 2, try to obtain the attraction regions of these threeroots.

P.S. An attraction region of a root is defined as the set of allinitial points which will eventually converge to the root.

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Matlab code for Multivariate Newton Raphson methodclear allclose allsyms x ysteady state equationfxyx3ygxyy3xNewton Raphson algorithmfxxydifffxfyxydifffygxxydiffgxgyxydiffgyinitial guess for Newton Raphsonx02y02fprintfFor initial guess xf and yfx0y0err1 c0loop for Newton Raphson    See Answer
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