◆ Dka()

Roots of a polynomial (complex coefficients) (DKA method)

Purpose: This routine computes all roots of a polynomial p(z) with complex coefficients by DKA (Durand-Kerner-Aberth) method.
p(z) = a0*z^n + a1*z^(n-1) + ... + an

Parameters

[in]	N	Degree of polynomial. (N >= 1)
[in]	A()	Array A(LA - 1) (LA >= N + 1) Complex coefficient vector of p(z) (a0 to an).
[out]	Z()	Array Z(LZ - 1) (LZ >= N) The obtained zeros.
[out]	Info	= 0: Successful exit. = -1: The argument N had an illegal value. (N <= 0) = -2: The argument A() is invalid. = -3: The argument Z() is invalid. = 1: Maximum number of iterations exceeded.
[out]	Iter	(Optional) Number of iterations required to converge.
[in]	MaxIter	(Optional) Maximum number of iterations. (default = 10 * N) If MaxIter <= 0, the default value will be used.

Reference: (Japanese book) Masatake Mori "FORTRAN77 Numerical Calculation Programming (augmented edition)" Iwanami Shoten (1987)

Example Program: Solve the following algebraic equation.
x^3 + (-19-14i)*x^2 + (67+191i)*x + 116-612i = 0

The exact solutions are 8 + 4i, 4 + 9i and 7 + i.
Sub Ex_Dka()

Const N As Long = 3

Dim A(N) As Complex, Z(N - 1) As Complex

Dim Iter As Long, Info As Long, I As Long

A(0) = Cmplx(1): A(1) = Cmplx(-19, -14): A(2) = Cmplx(67, 191)

A(3) = Cmplx(116, -612)

Call Dka(N, A(), Z(), Info, Iter)

For I = 0 To N - 1

Debug.Print Creal(Z(I)), Cimag(Z(I))

Next

Debug.Print "Iter =", Iter, "Info =", Info

End Sub