DekkerBrentSolver<T> Class

public sealed class DekkerBrentSolver<T> : RootBracketingSolver<T>
where T : Object, INumber<T>

Public NotInheritable Class DekkerBrentSolver(Of T As {Object, INumber(Of T)})
	Inherits RootBracketingSolver(Of T)

generic<typename T>
where T : Object, INumber<T>
public ref class DekkerBrentSolver sealed : public RootBracketingSolver<T>

[<SealedAttribute>]
type DekkerBrentSolver<'T when 'T : Object and INumber<'T>> = 
    class
        inherit RootBracketingSolver<'T>
    end

Inheritance

Object  →  ManagedIterativeAlgorithm<T, T, SolutionReport<T, T>>  →  IterativeAlgorithm<T>  →  EquationSolver<T>  →  RootBracketingSolver<T>  →  DekkerBrentSolver<T>

Type Parameters

T

Use the DekkerBrentSolver class to find a root of a function if you have an interval that includes a root with certainty. This is one of the more robust of the root bracketing solver algorithms. The RobustSolver, based on TOMS algorithm 748, is generally somewhat faster and more reliable.

DekkerBrentSolver inherits from RootBracketingSolver, which in turn inherits from IterativeAlgorithm<T>. All properties of IterativeAlgorithm<T> are available. The AbsoluteTolerance and RelativeTolerance properties set the desired precision as specified by the ConvergenceCriterion property. The default value for both tolerances is SqrtEpsilon (roughly 10^-8). MaxIterations sets the maximum number of iterations.

The TargetFunction property is a function of one variable that specifies the function we want to find a root for. The LowerBound and UpperBound properties specify the bounds of the bracketing interval. The target function must have a different sign at each end of this interval.

The Solve() method performs the actual approximation of the root. This method returns the best approximation that was found. The Status property indicates whether the algorithm was successful. The EstimatedError property gives an upper bound for the difference between the approximated and the actual root.

The Dekker-Brent method is the most advanced of the root bracketing algorithms. It combines the robustness of the bisection method with the increased speed of the regula falsi (false positioning) method.

At each iteration, either a bisection or a regula falsi step is taken, depending on the behavior of the algorithm up to that point. As a result, the Dekker-Brent method will converge as fast as the best case regula falsi method at its best, and as slow as the bisection method at its worst.

Reference