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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

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I think this can answer part 1 of your question: http://www.mathworks.nl/help/symbolic/jacobian.html

Of course it will require the Matlab symbolic toolbox.

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I guess this is the best solution, strictly speaking, if the user is not at all interesting in knowing how to do the math and is using MATLAB... It's a bit of a shame though if this is the case... – rschwieb Oct 23 '12 at 12:25

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