Package com.opengamma.strata.math.impl.rootfinding

Class EigenvaluePolynomialRootFinder

  • All Implemented Interfaces:
    Polynomial1DRootFinder<Double>
    public class EigenvaluePolynomialRootFinder
extends Object
implements Polynomial1DRootFinder<Double>
    The eigenvalues of a matrix $\mathbf{A}$ are the roots of the characteristic polynomial $P(x) = \mathrm{det}[\mathbf{A} - x\mathbb{1}]$. For a polynomial $$ \begin{align*} P(x) = \sum_{i=0}^n a_i x^i \end{align*} $$ an equivalent polynomial can be constructed from the characteristic polynomial of the matrix $$ \begin{align*} A = \begin{pmatrix} -\frac{a_{m-1}}{a_m} & -\frac{a_{m-2}}{a_m} & \cdots & -\frac{a_{1}}{a_m} & -\frac{a_{0}}{a_m} \\ 1 & 0 & \cdots & 0 & 0 \\ 0 & 1 & \cdots & 0 & 0 \\ \vdots & & \cdots & & \vdots \\ 0 & 0 & \cdots & 1 & 0 \end{pmatrix} \end{align*} $$ and so the roots are found by calculating the eigenvalues of this matrix.