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Re: symbolic derivatives

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  • Subject: [mg333] Re: [mg320] symbolic derivatives
  • From: Jerry Keiper <keiper>
  • Date: Thu, 15 Dec 1994 14:43:20 -0600

  > Although these functions are continuous, FindRoot gives an error
  > message to the effect that the Jacobian matrix (needed for
  > Newton's method), cannot be symbollically determined; it also
  > suggests trying with 2 initial guesses insteadof one (so the
  > secant method can be utilized).  I conclude that Mathematica
  > cannot differentiate continuously differentiable functions which
  > are subject to conditions.

  > I prefer to use Newton's method if possible.  Does anyone know
  > of a package thatwill solve nonlinear algebraic equations?
  > Ideally such a package should allow one to provide the Jacobian
  > matrix oneself.

You don't need a package.  FindRoot already has an option to specify
the Jacobian.  The default is Automatic, but you can specify it yourself
if it won't do it automatically.  

In[1]:= FindRoot[Sin[Abs[x]] == 3/4, {x, 1},
		Jacobian -> {{Sign[x] Cos[Abs[x]]}}]

Out[1]= {x -> 0.848062}

Jerry B. Keiper
keiper at
Wolfram Research, Inc.

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