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InterpolateRoot

InterpolateRoot[lhsrhs, {x, x0, x1}]
searches for a numerical solution to the equation lhsrhs using x0 and x1 as the first two values of x.
  • InterpolateRoot gives the solution as a rule of the form x->sol.
  • InterpolateRoot[expr, {x, x0, x1}] will search for a root of the equation expr0.
  • InterpolateRoot searches for a solution using inverse cubic interpolation of the last four data points. It does not use derivative information.
  • InterpolateRoot works very slowly when the solution is a multiple root.
  • InterpolateRoot is not as robust as FindRoot. However, it is useful when the location of the root is approximately known, each evaluation of the function is expensive, and high precision is desired.
  • If the equation and starting values are real, then InterpolateRoot will search only for real roots, otherwise it will search for complex roots.
  • The following options can be given:
AccuracyGoalAutomaticthe accuracy sought
MaxIterations15maximum number of iterations to use
ShowProgressFalsewhether progress is to be monitored
WorkingPrecision40the precision to use in internal computations
  • The setting for AccuracyGoal refers to the accuracy of the root rather than the magnitude of the residual at the root.
  • The precision used in internal computations typically varies from a little more than machine precision at the beginning to the setting for WorkingPrecision at the end.
  • If InterpolateRoot does not succeed in finding a solution to the desired accuracy within MaxIterations steps, it returns the most recent approximation found.
  • With ShowProgress->True, InterpolateRoot will print {accuracy, x} followed by {precision, extraprecision, delta}, where:
accuracyestimate of the accuracy of the current approximation to the solution
xcurrent approximation to the solution
precisioncurrent working precision
extraprecisionnumber of extra digits of precision being used
deltapredicted change in the approximation during the next iteration