Suppose $f(x,y) = x^2+xy+y^2$. How do you write this as two functions $f_{1}(x,y)$ and $f_{2}(x,y)$? I am trying to use Newton's method for $f(x,y)$.
Writing a multivariable function as two functions
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multivariable-calculus
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1Apparently you misunderstood how to compute the gradient. Do you know how to do partial derivatives? – 2012-04-19
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0@J.M.: I know how to do that. But you just need to set the gradients equal to 0? Not the actual function? – 2012-04-19
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0Depends on what you're trying to do. Are you optimizing $f(x,y)$? – 2012-04-19
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0@J.M. Yeah trying to find the minimum of $f(x,y)$. – 2012-04-19
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0Apply Newton's method to the gradient of $f$, ie, $(\frac{\partial f(x,y)}{\partial x}, \frac{\partial f(x,y)}{\partial y})$. – 2012-04-19