Root Bracketing Solver<T> Class
Represents the abstract base class for root finders for real
functions of one variable that use root bracketing.
Definition
Namespace: Numerics.NET.EquationSolvers.Generic
Assembly: Numerics.NET.Generic (in Numerics.NET.Generic.dll) Version: 9.0.1
C#
Assembly: Numerics.NET.Generic (in Numerics.NET.Generic.dll) Version: 9.0.1
public abstract class RootBracketingSolver<T> : EquationSolver<T>
where T : Object, INumber<T>
- Inheritance
- Object → ManagedIterativeAlgorithm<T, T, SolutionReport<T, T>> → IterativeAlgorithm<T> → EquationSolver<T> → RootBracketingSolver<T>
- Derived
Type Parameters
- T
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. |
TOM | 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
Root | Constructs a new RootBracketingSolver object. |
Root | Constructs a new RootBracketingSolver object for the specified target function and convergence parameters. |
Root | Constructs a new RootBracketingSolver object for the specified target function and convergence parameters. |
Properties
Absolute |
Gets or sets the absolute tolerance used in the
convergence test.
(Inherited from IterativeAlgorithm<T>) |
Convergence |
Gets or sets a value specifying the criterion that is
to be used in the convergence test for the algorithm.
(Inherited from IterativeAlgorithm<T>) |
Convergence |
Gets the convergence test for the algorithm.
(Inherited from IterativeAlgorithm<T>) |
Convergence |
Gets the collection of convergence tests for the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Current |
Gets the estimated error of the approximation of the result
at the current iteration.
(Inherited from IterativeAlgorithm<T>) |
Current |
Gets the lower bound of the convergence interval
at the current iteration.
(Inherited from EquationSolver<T>) |
Current | Gets or sets the value of the target function at the lower bound of the interval. |
Current |
Gets the approximation of the result at the current iteration.
(Inherited from IterativeAlgorithm<T>) |
Current |
Gets the upper bound of the convergence interval
at the current iteration.
(Inherited from EquationSolver<T>) |
Current | Gets or sets the value of the target function at the upper bound of the interval. |
Estimated |
Gets a value indicating the size of the absolute
error of the result.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Evaluations |
Gets the number of evaluations needed to execute the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Evaluations |
Gets the number of evaluations still available.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Has |
Indicates whether the degree of parallelism is a property that is shared
across instances.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Iterations |
Gets the number of iterations needed by the
algorithm to reach the desired accuracy.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Iterations |
Gets the number of iterations remaining.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Lower |
Gets or sets the lower bound for the solution.
(Inherited from EquationSolver<T>) |
Max |
Gets or sets the maximum degree of parallelism enabled by this instance.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Max |
Gets or sets the maximum number of evaluations during the calculation.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Max | Gets or sets the maximum number of iterations
to use when approximating the roots of the target
function.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Min |
Gets or sets the minimum iterations that have to be performed.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Parallel |
Gets or sets the configuration for the parallel behavior of the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Relative |
Gets or sets the relative tolerance used in the
convergence test.
(Inherited from IterativeAlgorithm<T>) |
Result |
Gets the result of an algorithm after it has executed.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Right |
Gets or sets the value of the target function to solve for.
(Inherited from EquationSolver<T>) |
Solution |
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>) |
Target |
Gets or sets the target function for the EquationSolver.
(Inherited from EquationSolver<T>) |
Throw |
Gets or sets whether to throw an
exception when the algorithm fails to converge.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Upper |
Gets or sets the upper bound for the solution.
(Inherited from EquationSolver<T>) |
Methods
Equals | Determines whether the specified object is equal to the current object. (Inherited from Object) |
Error |
Returns the estimated error for testing whether the algorithm has converged.
(Overrides IterativeAlgorithm<T>.ErrorEvaluator()) |
Evaluate |
Evaluates the target function and increments the number of evaluations.
(Inherited from EquationSolver<T>) |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
Get | Serves as the default hash function. (Inherited from Object) |
Get | Gets the Type of the current instance. (Inherited from Object) |
Increment |
Increments the number of evaluations by one.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Increment |
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<T>.Iterated()) |
Memberwise | 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<T>.OnInit()) |
Report |
Reports that the algoritm has failed. No further iterations will be performed.
(Overrides IterativeAlgorithm<T>.ReportFailure(AlgorithmStatus)) |
Report |
Records the results of an algorithm in case it fails.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Report |
Records the results of an algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Report |
Reports that the algoritm has succeeded. No further iterations will be performed.
(Overrides IterativeAlgorithm<T>.ReportSuccess()) |
Report |
Records the results of a algorithm that converged successfully.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Reset |
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( |
Runs the algorithm using the specified parallelization options.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Set |
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<T>) |
Solve( |
Attempts to find the point where the target function equals the specified value.
(Inherited from EquationSolver<T>) |
Test |
Checks whether the algorithm has converged.
(Inherited from IterativeAlgorithm<T>) |
Thread |
Increments the number of evaluations by one.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Thread |
Increments the number of evaluations by the specified amount.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>) |
Throw |
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) |
Update |
Updates the current approximation in a point-wise convergence.
(Inherited from IterativeAlgorithm<T>) |
Update | Updates the lower bound and the corresponding value of the target function. |
Update | Updates the upper bound and the corresponding value of the target function. |
Value |
Returns the value to compare the estimated error to
when testing whether the algorithm has converged.
(Overrides IterativeAlgorithm<T>.ValueEvaluator()) |