# FindRoot

Usage

FindRoot[lhsrhs, {x, }] searches for a numerical solution to the equation lhsrhs, starting with x=.
FindRoot[{, , ... }, {{x, }, {y, }, ... }] searches for a numerical solution to the simultaneous equations .

Notes

• 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.
FindRoot returns a list of replacements for x, y, ... , in the same form as obtained from Solve.
FindRoot has attribute HoldAll.
FindRoot[lhsrhs, {x, , }] searches for a solution using and as the first two values of x, avoiding the use of derivatives.
FindRoot[lhsrhs, {x, , , }] searches for a solution, stopping the search if x ever gets outside the range to .
• 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.
• 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.
FindRoot[expr, ... ] will search for a root of the equation expr0.
• The following options can be given:
 the accuracy sought expression to evaluate whenever equations are evaluated Jacobian the Jacobian of the system MaxIterations 100 maximum number of iterations to use the precision sought expression to evaluate whenever a step is taken the precision to use in internal computations
• The default settings for AccuracyGoal and PrecisionGoal are WorkingPrecision/2.
• The setting for AccuracyGoal specifies the number of digits of accuracy to seek in both the value of the position of the root, and the value of the function at the root.
• The setting for PrecisionGoal specifies the number of digits of precision to seek in the value of the position of the root.
FindRoot continues until either of the goals specified by AccuracyGoal or PrecisionGoal is achieved.
• 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.
• Implementation notes: see Section A.9.4.
• Related package: NumericalMath`InterpolateRoot`.
• New in Version 1; modified in 5.