Parallel Bairstow root-finding methods for real polynomials (MT) More...

#include "rootfinding.hpp"

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Functions
auto	pbairstow_even_mt (const std::vector< double > &coeffs, std::vector< Vec2 > &vrs, const ginger::Options &options) -> std::pair< unsigned int, bool >
	Multi-threading Bairstow's method (even degree only)

Detailed Description

Parallel Bairstow root-finding methods for real polynomials (MT)

Function Documentation

extern

Multi-threading Bairstow's method (even degree only)

The pbairstow_even_mt function implements Bairstow's method for finding the roots of a real polynomial with an even degree using multi-threading.

Each thread handles one quadratic factor \( x^2 - r_i x - q_i \), applying:

\[ \begin{bmatrix} \Delta r_i \\ \Delta q_i \end{bmatrix} = -J_i^{-1} \begin{bmatrix} P_i \\ Q_i \end{bmatrix} \]

where \( P_i, Q_i \) are the remainders from synthetic division.

Parameters

[in]	coeffs	The `coeffs` parameter is a vector representing the coefficients of the polynomial. Each element of the vector corresponds to the coefficient of a term in the polynomial, starting from the highest degree term and ending with the constant term. For example, if the polynomial is `3x^2 + 2x + 1`, the coefficients vector would be `{3, 2, 1}`.
[in,out]	vrs	`vrs` is a vector of iterates, which represents the initial guesses for the roots of the polynomial. Bairstow's method will update these iterates iteratively until the desired tolerance is reached or the maximum number of iterations is reached.
[in]	options	The `options` parameter is an object of type `Options` which contains the maximum number of iterations (`max_iters`) and the tolerance (`tolerance`). These options are used to control the convergence criteria for Bairstow's method.

Returns: The function pbairstow_even_mt returns a std::pair<unsigned int, bool>. The first element of the pair represents the number of iterations performed, and the second element represents whether the method converged to a solution within the specified tolerance.