Lines Matching full:polynomial
24 * \brief This module provides a QR based polynomial solver.
39 and a QR based polynomial solver.
43 polynomials, computing estimates about polynomials and next the QR based polynomial
50 void roots_to_monicPolynomial( const RootVector& rv, Polynomial& poly )
63 evaluates a polynomial at a given point using stabilized Hörner method.
65 The following code: first computes the coefficients in the monomial basis of the monic polynomial that has the provided roots;
66 then, it evaluates the computed polynomial, using a stabilized Hörner method.
74 Real cauchy_max_bound( const Polynomial& poly )
76 provides a maximum bound (the Cauchy one: \f$C(p)\f$) for the absolute value of a root of the given polynomial i.e.
84 Real cauchy_min_bound( const Polynomial& poly )
86 provides a minimum bound (the Cauchy one: \f$c(p)\f$) for the absolute value of a non zero root of the given polynomial i.e.
93 \section QR polynomial solver class
94 Computes the complex roots of a polynomial by computing the eigenvalues of the associated companion matrix with the QR algorithm.
109 Therefore the current polynomial solver is guaranteed to provide a correct result only when the complex roots \f$r_1,r_2,...,r_d\f$ have distinct moduli i.e.
115 (double) floating types and small polynomial degree (<20).
121 -# a simple use of the polynomial solver is shown;
122 -# the accuracy problem with the QR algorithm is presented: a polynomial with almost conjugate roots is provided to the solver.
