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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Implift/durand_kerner.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Floating_Numbers;          use Standard_Floating_Numbers;
        !             2: with Standard_Complex_Vectors;           use Standard_Complex_Vectors;
        !             3:
        !             4: generic
        !             5:
        !             6:   with procedure Write ( step : in natural; z,res : in Vector );
        !             7:
        !             8:   -- DESCRIPTION :
        !             9:   --   This routine allows to write intermediate results after each iteration,
        !            10:   --   such as the step number, the approximations z and the residuals res.
        !            11:   --   If no output is wanted, supply an empty body for Write.
        !            12:
        !            13: procedure Durand_Kerner ( p : in Vector; z,res : in out Vector;
        !            14:                           maxsteps : in natural; eps : in double_float;
        !            15:                           nb : out natural );
        !            16:
        !            17: -- DESCRIPTION :
        !            18: --   This routine computes all roots of a given polynomial
        !            19: --   in one unknown, applying the method of Durand Kerner.
        !            20: --   This method is also known as the method of Weierstrass.
        !            21:
        !            22: -- ON ENTRY :
        !            23: --   p           the polynomial defined by
        !            24: --                 p[k] + p[k+1]*x + p[k+2]*x^2 + .. + p[k+n]*x^n,
        !            25: --               with k = p'first;
        !            26: --   z           initial approximations for the roots;
        !            27: --   res         the residuals of the roots;
        !            28: --   maxsteps    is the maximum number of steps that are allowed;
        !            29: --   eps         the required accuracy.
        !            30:
        !            31: -- ON RETURN :
        !            32: --   z           the computed roots;
        !            33: --   res         the residuals of the roots;
        !            34: --   nb          the number of steps.