LocateRoot• LocateRoot[f, {x,  }] searches for a numerical solution to the equation f  0, starting with x =  .
• LocateRoot[f, {x,  ,  }] searches for a solution using  and  as the first two values of x. This form must be used if symbolic derivatives of the equation cannot be found.
• LocateRoot[f, {x, xstart, xmin, xmax}] searches for a solution, stopping the search if x ever gets outside the range xmin to xmax.
• LocateRoot[{ ,  , ... }, {x,  }, {y,  }, ... ] searches for a numerical solution to the simultaneous equations  . • LocateRoot returns a list of replacements for x, y, ... , in the same form as obtained from SolveEquation.
• If you specify only one starting value of x, LocateRoot searches for a solution using Newton's method. If you specify two starting values, LocateRoot uses a variant of the secant method.
• If all equations and starting values are real, then LocateRoot will search only for real roots. If any are complex, it will also search for complex roots.
• You can always tell LocateRoot to search for complex roots by adding 0. I to the starting value.
• See also: LocateMinimum, SolveEquation, SolveODE.
Examples Using InstantCalculatorsHere are the InstantCalculators for the LocateRoot function. Enter the parameters for your calculation and click Calculate to see the result.
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Entering Commands DirectlyYou can paste a template for this command via the Text Input button on the LocateRoot Function Controller. These two curves intersect at one point.
This finds a numerical approximation to the x coordinate of the intersection point. The -0.5 is the initial guess.
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Trigonometric equations typically have an infinite number of roots. If you start sufficiently close to a particular root of an equation, LocateRoot will find that root.
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Starting closer to another root will give a different solution.
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You can restrict LocateRoot so that it looks for solutions in one particular region only. Here the initial guess is  and the solution is supposed to be between  and  . There is no such solution.
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This is what happens when LocateRoot can find no solutions at all.
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If you want LocateRoot to use complex values in its search, then you need to give a complex starting value.
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You can use the secant method by giving two starting values.
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This finds a solution to a set of simultaneous equations. It is a good idea to avoid taking the starting values for x and y to be equal or to take any other "special" combinations of values.
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