Cpqr79 Cpzero Dka Rpqr79 Rpzero Rpzero2

Cpqr79() Sub Cpqr79 ( N As  Long, A() As  Complex, Z() As  Complex, Info As  Long  ) Roots of a polynomial (complex coefficients) (by computing the eigenvalues of the companion matrix) Purpose This routine computes all roots of a polynomial p(z) with complex coefficients by computing the eigenvalues of the companion matrix. 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: Failed to converge within maximum number (30) of QR iterations on some eigenvalue of the companion matrix. Reference SLATEC 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_Cpqr79() Const N As Long = 3 Dim A(N) As Complex, Z(N - 1) As Complex Dim 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 Cpqr79(N, A(), Z(), Info) For I = 0 To N - 1 Debug.Print Creal(Z(I)), Cimag(Z(I)) Next Debug.Print "Info =", Info End Sub Example Results 4 9.00000000000001 7.99999999999999 3.99999999999998 7.00000000000001 1.00000000000001 Info = 0