# using Newton's method for three -dimensional system in matlab

Find the Jacobian matrix $J(x, y, z)$ for the functions

$f(x, y, z) = x^2 + y^2 + z^2 − 9 = 0,$

$g(x, y, z) = xyz − 1 = 0,$

$h(x, y, z) = x + y − z^2 = 0.$

Then using Newton’s method for nonlinear systems, starting with different initial guesses, find four solutions of the above nonlinear set of equations with the accuracy of four decimal places. To find the solutions write a Matlab script to do Newton iteration for this as a three-dimensional system.

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What have you tried? I have no interest in this system, so I have no desire to find the Jacobian or solve it. However, I'd be more than happy to direct you along the right path if you enlighten me as to where you are having issues. –  Arkamis Oct 22 '12 at 17:09