public class Bisection extends java.lang.Object implements MonadicFunctionRootFinder
The Method of Bisection is a root-finding method which requires an initial interval [x0,x1] bracketing a root and that the function be continuous in that interval.
An updated estimate of the root value is computed by using the midpoint of the two previous values. Depending upon the sign of the function at the interval midpoint, the midpoint replaces either the lower interval value (if f(midpoint) < 0) or the upper interval value (if f(midpoint) > 0). This bisection process halves the search interval on each iteration
If the function whose root is being sought has a derivative at each point in the interval, the Method of Secants or Brent's Method is a better choice.
Constructor and Description |
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Bisection()
Constructor if RootFinder interface used.
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Modifier and Type | Method and Description |
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static double |
bisection(double x0,
double x1,
double tol,
int maxIter,
MonadicFunction function)
Find root using the Method of Bisection.
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static double |
bisection(double x0,
double x1,
double tol,
int maxIter,
MonadicFunction function,
RootFinderConvergenceTest convergenceTest,
RootFinderIterationInformation iterationInformation)
Find root using the Method of Bisection.
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static double |
bisection(double x0,
double x1,
MonadicFunction function)
Find root using the Method of Bisection.
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double |
findRoot(double x0,
double x1,
double tol,
int maxIter,
MonadicFunction function,
MonadicFunction derivativeFunction,
RootFinderConvergenceTest convergenceTest,
RootFinderIterationInformation iterationInformation)
Implementation for
MonadicFunctionRootFinder interface. |
public static double bisection(double x0, double x1, double tol, int maxIter, MonadicFunction function, RootFinderConvergenceTest convergenceTest, RootFinderIterationInformation iterationInformation) throws java.lang.IllegalArgumentException
x0
- First approximation to root value.x1
- Second approximation to root value.tol
- Desired accuracy for root value.maxIter
- Maximum number of iterations.function
- Class implementing MonadicFunction
interface to provide function values.convergenceTest
- RootFinderConvergenceTest which
tests for convergence of the root-finding
process.iterationInformation
- Class implementing
RootFinderIterationInformation
for retrieving information about
each iteration of root finding
process. Set to null if you don't
want this information.java.lang.IllegalArgumentException
- if [x0,x1] cannot be expanded
to bracket a root or function
is null.
This implementation always starts by attempting to expand the root bracketing interval to enclose a root.
public static double bisection(double x0, double x1, double tol, int maxIter, MonadicFunction function) throws java.lang.IllegalArgumentException
x0
- First approximation to root value.x1
- Second approximation to root value.tol
- Desired accuracy for root value.maxIter
- Maximum number of iterations.function
- Class implementing MonadicFunction
interface to provide function values.java.lang.IllegalArgumentException
- if [x0,x1] cannot be expanded
to bracket a root or function
is null.
This implementation always starts by attempting to expand the root bracketing interval to enclose a root.
public static double bisection(double x0, double x1, MonadicFunction function) throws java.lang.IllegalArgumentException
x0
- First approximation to root value.x1
- Second approximation to root value.function
- Class implementing MonadicFunction
interface to provide function values.java.lang.IllegalArgumentException
- if [x0,x1] cannot be expanded
to bracket a root or function
is null.
This implementation always starts by attempting to expand the root bracketing interval to enclose a root. Up to 250 iterations are attempted with the convergence tolerance set to Constants.MACHEPS .
public double findRoot(double x0, double x1, double tol, int maxIter, MonadicFunction function, MonadicFunction derivativeFunction, RootFinderConvergenceTest convergenceTest, RootFinderIterationInformation iterationInformation) throws java.lang.IllegalArgumentException
MonadicFunctionRootFinder
interface.findRoot
in interface MonadicFunctionRootFinder
x0
- Left bracket value for root.x1
- Right bracket value for root.
Not used by some root-finder
(e.g., Newton/Raphson),
set to same value as x0 in those cases.tol
- Convergence tolerance.maxIter
- Maximum number of iterations.function
- MonadicFunction computes value for
function whose root is being sought.derivativeFunction
- MonadicFunction computes derivative
value for function whose root is
being sought. Currently used only
by Newton/Raphson, set to null for
other methods.convergenceTest
- RootFinderConvergenceTest which
tests for convergence of the root-finding
process.iterationInformation
- Method implementing the
RootFinderIterationInformation
interace. Allows retrieval of
function, function derivative, and
iteration number for each iteration
in the root-finding process.
Can be set to null if you don't want
to get that information.java.lang.IllegalArgumentException