This is documentation for Mathematica 4, which was
based on an earlier version of the Wolfram Language.

FindRoot

FindRoot[lhs==rhs, x, ] searches for a numerical solution to the equation lhs==rhs, starting with x=.

FindRoot[lhs==rhs, 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.

FindRoot[lhs==rhs, x, xstart, xmin, xmax] searches for a solution, stopping the search if x ever gets outside the range xmin to xmax.

FindRoot[, , ... , x, , y, , ... ] searches for a numerical solution to the simultaneous equations .

FindRoot returns a list of replacements for x, y, ... , in the same form as obtained from Solve.

FindRoot has attribute HoldAll.

If you specify only one starting value of x, FindRoot searches for a solution using Newton's method. If you specify two starting values, FindRoot uses a variant of the secant method.

If all equations and starting values are real, then FindRoot will search only for real roots. If any are complex, it will also search for complex roots.

You can always tell FindRoot to search for complex roots by adding 0. I to the starting value.

The following options can be given:

The default setting for AccuracyGoal is 10 digits less than WorkingPrecision.

If FindRoot does not succeed in finding a solution to the accuracy you specify within MaxIterations steps, it returns the most recent approximation to a solution that it found. You can then apply FindRoot again, with this approximation as a starting point.

The size of each step taken in Newton's method is multiplied by the setting given for DampingFactor.

See The Mathematica Book: Section 1.5.7, Section 1.6.3 and Section 3.9.6.

Implementation Notes: see section A.9.4.