FUNCTION APPROXIMATIONS PACKAGE SYMBOL

# InterpolateRoot

searches for a numerical solution to the equation using and as the first two values of x.

## DetailsDetails

• To use , you first need to load the Function Approximations Package using Needs["FunctionApproximations`"].
• gives the solution as a rule of the form .
• will search for a root of the equation expr==0.
• searches for a solution using inverse cubic interpolation of the last four data points. It does not use derivative information.
• works very slowly when the solution is a multiple root.
• 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 will search only for real roots, otherwise it will search for complex roots.
• The following options can be given:
•  AccuracyGoal Automatic the accuracy sought MaxIterations 15 maximum number of iterations to use ShowProgress False whether progress is to be monitored WorkingPrecision 40 the 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.
• The setting for WorkingPrecision may be exceeded to achieve the desired AccuracyGoal.
• If does not succeed in finding a solution to the desired accuracy within MaxIterations steps, it returns the most recent approximation found.
• With ShowProgress->True, will print followed by , where:
•  accuracy estimate of the accuracy of the current approximation to the solution x current approximation to the solution precision current working precision extraprecision number of extra digits of precision being used delta predicted change in the approximation during the next iteration

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

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Check:

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