Cpqr79 Cpzero Dka Rpqr79 Rpzero Rpzero2

Rpqr79() Sub Rpqr79 ( N As  Long, A() As  Double, Z() As  Complex, Info As  Long  ) Roots of a polynomial (real coefficients) (Companion matrix method) Purpose This routine computes all roots of a polynomial p(z) with real 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) Real 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^5 + 2*x^3 + 2*x^2 - 15*x + 10 = 0 The exact solutions are 1(double root), -2 and ±√5. Sub Ex_Rpqr79() Const N As Long = 5 Dim A(N) As Double, Z(N - 1) As Complex, S(N - 1) As Double Dim Info As Long, I As Long A(0) = 1: A(1) = 0: A(2) = 2: A(3) = 2: A(4) = -15: A(5) = 10 Call Rpqr79(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 -2 0 -2.1094237467878E-15 2.23606797749979 -2.1094237467878E-15 -2.23606797749979 0.999999999999999 2.75985349470833E-08 0.999999999999999 -2.75985349470833E-08 Info = 0