InterpolateRoot

• To use InterpolateRoot, you first need to load the Function Approximations Package using Needs["FunctionApproximations`"].

• 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:

• 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.

• The setting for WorkingPrecision may be exceeded to achieve the desired AccuracyGoal.

• 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: