This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Documentation / Mathematica / Built-in Functions / Numerical Computation / Equation Solving /

FindRoot

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

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

FilledSmallSquare If the starting point for a variable is given as a list, the values of the variable are taken to be lists with the same dimensions.

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

FilledSmallSquare FindRoot has attribute HoldAll.

FilledSmallSquare FindRoot[lhs==rhs, x, , ] searches for a solution using and as the first two values of x, avoiding the use of derivatives.

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

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

FilledSmallSquare 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.

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

FilledSmallSquare FindRoot[expr, ... ] will search for a root of the equation expr==0.

FilledSmallSquare The following options can be given:

FilledSmallSquare The default settings for AccuracyGoal and PrecisionGoal are WorkingPrecision/2.

FilledSmallSquare The setting for AccuracyGoal specifies the number of digits of accuracy to seek both in the value of the position of the root, and the value of the function at the root.

FilledSmallSquare The setting for PrecisionGoal specifies the number of digits of precision to seek in the value of the position of the root.

FilledSmallSquare FindRoot continues until either of the goals specified by AccuracyGoal or PrecisionGoal is achieved.

FilledSmallSquare 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.

FilledSmallSquare See Section 1.5.7, Section 1.6.3 and Section 3.9.6.

FilledSmallSquare Implementation Notes: see Section A.9.4.

FilledSmallSquare See also: NSolve, Solve, FindMinimum, FindInstance.

FilledSmallSquare Related package: NumericalMath`InterpolateRoot`.

FilledSmallSquare New in Version 1; modified in 5.0.

Further Examples