Class RootFinding

java.lang.Object

org.episteme.core.mathematics.analysis.rootfinding.RootFinding

public class RootFinding
extends Object

Root finding algorithms for solving f(x) = 0.

Implements Newton-Raphson, Bisection, and Secant methods.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
RootFinding()

Method Summary

Modifier and Type	Method	Description
static Real	bisection(Function<Real,Real> f, Real a, Real b, Real tolerance, int maxIterations)	Bisection method (bracketing method).
static Real	brent(Function<Real,Real> f, Real a, Real b, Real tolerance)	Brent's method - combination of bisection, secant, and inverse quadratic interpolation.
static Real	newtonRaphson(Function<Real,Real> f, Function<Real,Real> df, Real initialGuess, Real tolerance, int maxIterations)	Newton-Raphson method: xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ)
static Real	secant(Function<Real,Real> f, Real x0, Real x1, Real tolerance, int maxIterations)	Secant method: xₙ₊₁ = xₙ - f(xₙ) * (xₙ - xₙ₋₁) / (f(xₙ) - f(xₙ₋₁))

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

RootFinding

public RootFinding()

Method Details

newtonRaphson

public static Real newtonRaphson(Function<Real,Real> f,
 Function<Real,Real> df,
 Real initialGuess,
 Real tolerance,
 int maxIterations)

Newton-Raphson method: xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ)

Quadratic convergence near root. Requires derivative.

Parameters:

f - the function

df - the derivative of f

initialGuess - starting point

tolerance - convergence tolerance

maxIterations - maximum iterations

Returns:

approximate root, or null if not found

bisection

public static Real bisection(Function<Real,Real> f,
 Real a,
 Real b,
 Real tolerance,
 int maxIterations)

Bisection method (bracketing method).

Guaranteed convergence if f(a) and f(b) have opposite signs. Linear convergence but robust.

Parameters:

f - the function

a - left bracket

b - right bracket

tolerance - convergence tolerance

maxIterations - maximum iterations

Returns:

approximate root, or null if not found

secant

public static Real secant(Function<Real,Real> f,
 Real x0,
 Real x1,
 Real tolerance,
 int maxIterations)

Secant method: xₙ₊₁ = xₙ - f(xₙ) * (xₙ - xₙ₋₁) / (f(xₙ) - f(xₙ₋₁))

Superlinear convergence. Does not require derivative.

Parameters:

f - the function

x0 - first initial guess

x1 - second initial guess

tolerance - convergence tolerance

maxIterations - maximum iterations

Returns:

approximate root, or null if not found

brent

public static Real brent(Function<Real,Real> f,
 Real a,
 Real b,
 Real tolerance)

Brent's method - combination of bisection, secant, and inverse quadratic interpolation.

Best general-purpose root finder. Guaranteed convergence with superlinear speed.

Parameters:

f - the function

a - left bracket

b - right bracket

tolerance - convergence tolerance

Returns:

approximate root