Cpqr79 Cpzero Dka Rpqr79 Rpzero Rpzero2

Rpzero2() Sub Rpzero2 ( N As  Long, A() As  Double, Zr() As  Double, Zi() As  Double, IFlag As  Long, S() As  Double, Info As  Long, Optional Iter As  Long, Optional MaxIter As  Long = 0  ) Roots of a polynomial (real coefficients) (Netwon method) (complex type is not used) Purpose This routine computes all roots of a polynomial p(z) with real coefficients by Netwon method. p(z) = a0*z^n + a1*z^(n-1) + ... + an The obtained zeros are output to the separate real type variables for real and imaginary parts. 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). [in,out] Zr() Array Zr(LZr - 1) (LZr >= N) [in] Real parts of initial estimates for zeros. If these are unknown, set IFlag = 0 and it is not necessary to set estimates in Zr().   Note - Initial estimates must be separated, that is, distinct or not repeated. [out] Real parts of the zeros [in,out] Zi() Array Zi(LZi - 1) (LZi >= N) [in] Imaginary parts of initial estimates for zeros. If these are unknown, set IFlag = 0 and it is not necessary to set estimates in Zi().   Note - Initial estimates must be separated, that is, distinct or not repeated. [out] Imaginary parts of the obtained zeros. [in] IFlag Flag to indicate if initial estimates of zeros are input. = 0: No estimates are input. <> 0: Zr() and Zi() contain estimates of zeros. [out] S() Array S(LS - 1) (LS >= N) Error bound for Zr() and Zi(). [out] Info = 0: Successful exit. = -1: The argument N had an illegal value. (N < 1) = -2: The argument A() is invalid or had an illegal value. (A(0) = 0) = -3: The argument Zr() is invalid. = -4: The argument Zi() is invalid. = -6: The argument S() is invalid. = 1: Maximum number of iterations exceeded. Best current estimates of the zeros are in Zr() and Zi(). Error bounds in S() are not calculated. [out] Iter (Optional) Number of iterations required to converge. [in] MaxIter (Optional) Maximum number of iterations. (default = 25 * N) If MaxIter <= 0, the default value will be used. 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 ±√5i. Sub Ex_Rpzero2() Const N As Long = 5 Dim A(N) As Double, Zr(N - 1) As Double, Zi(N - 1) As Double, S(N - 1) As Double Dim IFlag As Long, Info As Long, I As Long A(0) = 1: A(1) = 0: A(2) = 2: A(3) = 2: A(4) = -15: A(5) = 10 IFlag = 0 Call Rpzero2(N, A(), Zr(), Zi(), IFlag, S(), Info) For I = 0 To N - 1 Debug.Print Zr(I), Zi(I), S(I) Next Debug.Print "Info =", Info End Sub Example Results 1.0000000135981 2.14625358292393E-08 1.26597932122911E-07 1.48298437403299E-18 2.23606797749979 8.99528943854828E-15 -2 1.15041631099093E-19 7.53855142372064E-15 7.94241311875315E-17 -2.23606797749979 9.06723080094738E-15 0.999999987046461 -2.24784161738852E-08 1.26578540844987E-07 Info = 0 Note - Only half precision for double roots.