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.

Examples

Using InstantCalculators

Here 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 Directly

You can paste a template for this command via the Text Input button on the LocateRoot Function Controller.

These two curves intersect at one point.

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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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The criterion LocateRoot uses for convergence to a root is how close the function is to zero. If the function is very flat, it may be close to zero before the variable is close enough to the root.

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Here LocateRoot stops when the value of the function is within the accuracy goal (6 digits) of zero, but the root is only good to one decimal place.

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THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.