fr.cnes.sirius.patrius.math.analysis.solver

Class PolynomialRootsFinder

java.lang.Object

fr.cnes.sirius.patrius.math.analysis.solver.PolynomialRootsFinder

public final class PolynomialRootsFinder
extends Object

PolynomialRootsFinder computes the roots of the polynomial p represented by an array of coefficients, starting with the coefficient of greater degree. A coefficient of 0 indicates that an intermediate power is not present in the equation. It can compute either just the real part of the roots, or the full complex solution.

In this solver, the roots of the polynomial are calculated by computing the eigenvalues of the companion matrix A:

A = diag(ones(n-1, 1), -1); A(1,:) = -p(2:n+1)./p(1); r = eig(A);

The results produced are the exact eigenvalues of a matrix within roundoff error of the companion matrix, A. However, this does not mean that they are the exact roots of a polynomial whose coefficients are within roundoff error of those in p.

Since:

4.17

Author:

Thibaut BONIT

Method Summary

Modifier and Type	Method and Description
static Complex[]	findRootsComplexPolynomial(double[] coefficients) Given a list of coefficients of a polynomial (in decreasing order of degree), this method computes its COMPLEX roots.
static double[]	findRootsRealPolynomial(double[] coefficients) Given a list of coefficients of a polynomial (in decreasing order of degree), this method computes its REAL component of the roots.

Methods inherited from class java.lang.Object

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

Method Detail

findRootsRealPolynomial

public static double[] findRootsRealPolynomial(double[] coefficients)

Given a list of coefficients of a polynomial (in decreasing order of degree), this method computes its REAL component of the roots.

Parameters:

coefficients - List of coefficients of the polynomial (in decreasing order).

Returns:

the list of real roots

findRootsComplexPolynomial

public static Complex[] findRootsComplexPolynomial(double[] coefficients)

Given a list of coefficients of a polynomial (in decreasing order of degree), this method computes its COMPLEX roots.

Parameters:

coefficients - List of coefficients of the polynomial (in decreasing order).

Returns:

the list of complex roots