aberth.hpp file
Functions
- auto initial_aberth(const std::vector<double>& coeffs) -> std::vector< std::complex< double >> -> auto
- Initial guess for the Aberth-Ehrlich method.
- auto aberth(const std::vector<double>& coeffs, std::vector<std::complex<double>>& zs, const Options& options) -> std::pair< unsigned int, bool > -> auto
- Single-threading Aberth-Ehrlich method.
- auto aberth_mt(const std::vector<double>& coeffs, std::vector<std::complex<double>>& zs, const Options& options) -> std::pair< unsigned int, bool > -> auto
- Multi-threading Aberth-Ehrlich method.
Function documentation
auto initial_aberth(const std::vector<double>& coeffs) -> std::vector< std::complex< double >>
Initial guess for the Aberth-Ehrlich method.
| Parameters | |
|---|---|
| coeffs in | The coeffs parameter is a vector of doubles that represents the coefficients of a polynomial. |
| Returns | The function initial_aberth returns a vector of Complex numbers. |
The initial_aberth function calculates the initial values for the Aberth-Ehrlich method for finding the roots of a polynomial.
auto aberth(const std::vector<double>& coeffs, std::vector<std::complex<double>>& zs, const Options& options) -> std::pair< unsigned int, bool >
Single-threading Aberth-Ehrlich method.
| Parameters | |
|---|---|
| coeffs in | The coeffs parameter is a vector representing the coefficients of a polynomial. Each element of the vector corresponds to 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 + |
| zs in | zs is a vector of complex numbers representing the initial guesses for the roots of the polynomial. The function will update these values iteratively to converge to the actual roots. |
| options in | The options parameter is an object of type Options that contains the maximum number of iterations (max_iters) and the tolerance (tolerance). These options control the convergence criteria for the Aberth-Ehrlich method. |
| Returns | The aberth function 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. |
The aberth function is a multi-threaded implementation of the Aberth-Ehrlich method for finding the roots of a polynomial.
Aberth's method is a method for finding the roots of a polynomial that is robust but requires complex arithmetic even if the polynomial is real. This is because it starts with complex initial approximations.
auto aberth_mt(const std::vector<double>& coeffs, std::vector<std::complex<double>>& zs, const Options& options) -> std::pair< unsigned int, bool >
Multi-threading Aberth-Ehrlich method.
| Parameters | |
|---|---|
| coeffs in | The coeffs parameter is a vector representing the coefficients of a polynomial. Each element of the vector corresponds to 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 + |
| zs in | zs is a vector of complex numbers representing the initial guesses for the roots of the polynomial. The function will update these values iteratively to converge to the actual roots. |
| options in | The options parameter is an object of type Options that contains the maximum number of iterations (max_iters) and the tolerance (tolerance). These options control the convergence criteria for the Aberth-Ehrlich method. |
| Returns | The aberth function 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. |
The aberth function is a multi-threaded implementation of the Aberth-Ehrlich method for finding the roots of a polynomial.
Aberth's method is a method for finding the roots of a polynomial that is robust but requires complex arithmetic even if the polynomial is real. This is because it starts with complex initial approximations.