RootBracketingSolver Class

Represents the abstract base class for root finders for real functions of one variable that use root bracketing.

Definition

Namespace: Extreme.Mathematics.EquationSolvers
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23

public abstract class RootBracketingSolver : EquationSolver

Visual Basic

Public MustInherit Class RootBracketingSolver
	Inherits EquationSolver

C++/CLI

public ref class RootBracketingSolver abstract : public EquationSolver

[<AbstractClassAttribute>]
type RootBracketingSolver = 
    class
        inherit EquationSolver
    end

Inheritance: Object → ManagedIterativeAlgorithm<Double, Double, SolutionReport<Double, Double>> → ManagedIterativeAlgorithm<Double> → IterativeAlgorithm → EquationSolver → RootBracketingSolver

Derived: Extreme.Mathematics.EquationSolvers.BisectionSolver
Extreme.Mathematics.EquationSolvers.DekkerBrentSolver
Extreme.Mathematics.EquationSolvers.RegulaFalsiSolver
Extreme.Mathematics.EquationSolvers.Toms748Solver

Remarks

When two points are known where the target function has different signs, the target function has a root in the interval between the two points, provided the target function is continuous.

Root bracketing root finders use this property by generating smaller and smaller intervals until the length of the interval is smaller than the requested tolerance.

There are three main root bracketing methods. Each method is implemented in a RootBracketingSolver derived class as follows:

Method	Description
Bi-section method	Iteratively bisects the current bracketing interval and proceeds with the subinterval that still brackets the root.
Regula falsi method	Determines a new interval by approximating the target function by a line. The bracketing interval is divided at the point where this line crosses the X-axis.
Dekker-Brent method	Uses a combination of bi-section and inverse quadratic interpolation. This is one of the fastest and most reliable methods.
TOMS Algorithm 748	Uses a combination of bi-section, inverse quadratic, and inverse cubic interpolation. This is usually the fastest and most reliable method.

RootBracketingSolver is an abstract class that cannot be instantiated directly. Use one of the derived classes instead.

Constructors

RootBracketingSolver()	Constructs a new RootBracketingSolver object.
RootBracketingSolver(Func<Double, Double>, Double, Double)	Constructs a new RootBracketingSolver object for the specified target function and convergence parameters.
RootBracketingSolver(Func<Double, Double>, Double, Double, ConvergenceCriterion, Double)	Constructs a new RootBracketingSolver object for the specified target function and convergence parameters.

Properties

AbsoluteTolerance	Gets or sets the absolute tolerance used in the convergence test. (Inherited from IterativeAlgorithm)
ConvergenceCriterion	Gets or sets a value specifying the criterion that is to be used in the convergence test for the algorithm. (Inherited from IterativeAlgorithm)
ConvergenceTest	Gets the convergence test for the algorithm. (Inherited from IterativeAlgorithm)
ConvergenceTests	Gets the collection of convergence tests for the algorithm. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
CurrentError	Gets the estimated error of the approximation of the result at the current iteration. (Inherited from IterativeAlgorithm)
CurrentLowerBound	Gets the lower bound of the convergence interval at the current iteration. (Inherited from EquationSolver)
CurrentLowerBoundValue	Gets or sets the value of the target function at the lower bound of the interval.
CurrentResult	Gets the approximation of the result at the current iteration. (Inherited from IterativeAlgorithm)
CurrentUpperBound	Gets the upper bound of the convergence interval at the current iteration. (Inherited from EquationSolver)
CurrentUpperBoundValue	Gets or sets the value of the target function at the upper bound of the interval.
EstimatedError	Gets a value indicating the size of the absolute error of the result. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
EvaluationsNeeded	Gets the number of evaluations needed to execute the algorithm. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
EvaluationsRemaining	Gets the number of evaluations still available. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
HasSharedDegreeOfParallelism	Indicates whether the degree of parallelism is a property that is shared across instances. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
IterationsNeeded	Gets the number of iterations needed by the algorithm to reach the desired accuracy. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
IterationsRemaining	Gets the number of iterations remaining. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
LowerBound	Gets or sets the lower bound for the solution. (Inherited from EquationSolver)
MaxDegreeOfParallelism	Gets or sets the maximum degree of parallelism enabled by this instance. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
MaxEvaluations	Gets or sets the maximum number of evaluations during the calculation. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
MaxIterations	Gets or sets the maximum number of iterations to use when approximating the roots of the target function. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
MinIterations	Gets or sets the minimum iterations that have to be performed. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ParallelOptions	Gets or sets the configuration for the parallel behavior of the algorithm. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
RelativeTolerance	Gets or sets the relative tolerance used in the convergence test. (Inherited from IterativeAlgorithm)
Result	Gets the result of an algorithm after it has executed. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
RightHandSide	Gets or sets the value of the target function to solve for. (Inherited from EquationSolver)
SolutionReport	Gets the result of an algorithm after it has executed. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Status	Gets the AlgorithmStatus following an execution of the algorithm. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
TargetFunction	Gets or sets the target function for the EquationSolver. (Inherited from EquationSolver)
ThrowExceptionOnFailure	Gets or sets a value indicating whether to throw an exception when the algorithm fails to converge. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
UpperBound	Gets or sets the upper bound for the solution. (Inherited from EquationSolver)

Methods

Equals	Determines whether the specified object is equal to the current object. (Inherited from Object)
ErrorEvaluator	Returns the estimated error for testing whether the algorithm has converged. (Overrides IterativeAlgorithm.ErrorEvaluator())
Evaluate	Evaluates the target function and increments the number of evaluations. (Inherited from EquationSolver)
Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object)
GetHashCode	Serves as the default hash function. (Inherited from Object)
GetType	Gets the Type of the current instance. (Inherited from Object)
IncrementEvaluations()	Increments the number of evaluations by one. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
IncrementEvaluations(Int32)	Increments the number of evaluations by the specified amount. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Iterate	Performs one iteration of the algorithm. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Iterated	Performs tasks after the iteration is completed, but before the status of the algorithm is finalized. (Overrides IterativeAlgorithm.Iterated())
MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object)
OnConvergence	Performs any tasks after the main algorithm has converged. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
OnFailure	Performs any tasks after the main algorithm has failed to converge. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
OnInit	Performs initialization tasks when the algorithm is first run. (Overrides IterativeAlgorithm.OnInit())
ReportFailure(AlgorithmStatus)	Reports that the algoritm has failed. No further iterations will be performed. (Overrides IterativeAlgorithm.ReportFailure(AlgorithmStatus))
ReportFailure(T, TError, AlgorithmStatus)	Records the results of an algorithm in case it fails. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ReportResult	Records the results of an algorithm. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ReportSuccess()	Reports that the algoritm has succeeded. No further iterations will be performed. (Overrides IterativeAlgorithm.ReportSuccess())
ReportSuccess(T, TError)	Records the results of a algorithm that converged successfully. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ResetEvaluations	Resets the number of evaluations to zero. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Restart	Prepares the algorithm to be run again with possibly different inputs. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Run()	Runs the algorithm. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Run(ParallelOptions)	Runs the algorithm using the specified parallelization options. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
SetResult	Sets the results of an algorithm's execution. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Solve()	Attempts to find a root or zero of the target function. (Inherited from EquationSolver)
Solve(Double)	Attempts to find the point where the target function equals the specified value. (Inherited from EquationSolver)
TestConvergence	Checks whether the algorithm has converged. (Inherited from IterativeAlgorithm)
ThreadSafeIncrementEvaluations()	Increments the number of evaluations by one. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ThreadSafeIncrementEvaluations(Int32)	Increments the number of evaluations by the specified amount. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ThrowConvergenceException	Interprets the AlgorithmStatus and throws the appropriate exception. (Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ToString	Returns a string that represents the current object. (Inherited from Object)
UpdateCurrentResult	Updates the current approximation in a point-wise convergence. (Inherited from IterativeAlgorithm)
UpdateLowerBound	Updates the lower bound and the corresponding value of the target function.
UpdateUpperBound	Updates the upper bound and the corresponding value of the target function.
ValueEvaluator	Returns the value to compare the estimated error to when testing whether the algorithm has converged. (Overrides IterativeAlgorithm.ValueEvaluator())