Dfzero Dfzero_r

Dfzero() Sub Dfzero ( F As  LongPtr, B As  Double, C As  Double, R As  Double, Re As  Double, Ae As  Double, Info As  Long  ) Solution of a single general nonlinear equation Purpose This routine searches for a zero of a function f(x) between the given values B and C until the width of the interval [B, C] has collapsed to within a tolerance specified by the stopping criterion, abs(B - C) <= 2*(Re*abs(B) + Ae). It is designed primarily for problems where f(B) and f(C) have opposite signs. The method used is an efficient combination of bisection and the secant rule. Parameters [in] F User supplied function which evaluates f(x) for the equation f(x) = 0 defined as follows: Function F(X As Double) As Double F = computed function value f(x) End Function X should not be changed. [in,out] B [in] Lower endpoint of the initial interval. [out] Lower endpoint of the final interval (the approximation to a zero). [in,out] C [in] Upper endpoint of the initial interval. [out] Upper endpoint of the final interval. [in] R A (better) guess of a zero of f which could help in speeding up convergence. When no better guess is known, it is recommended that R be set to B or C. [in] Re Relative error used for the stopping criterion. If the requested Re is less than machine precision, then it is set to approximately machine precision. [in] Ae Absolute error used in the stopping criterion. If the given interval [B, C] contains the origin, then a nonzero value should be chosen for Ae. [out] Info = 0: Successful exit. = 1: f(x) = 0, however the interval may not have collapsed to the requested tolerance. = 2: B may be near a singular point of f(x). = 3: No change in sign of f(x) was found although the interval. = 4: Too many (> 500) function evaluations used. Reference D. Kahaner, C. Moler, S. Nash, "Numerical Methods and Software", Prentice-Hall (1989) Example Program Find the root of the following equation in the interval [1, 3]. x^3 - 2x - 5 = 0 Function FDfzero(X As Double) As Double FDfzero = X ^ 3 - 2 * X - 5 End Function Sub Ex_Dfzero() Dim B As Double, C As Double, R As Double, Re As Double, Ae As Double Dim Info As Long B = 1: C = 3: R = B Re = 0: Ae = 0 Call Dfzero(AddressOf FDfzero, B, C, R, Re, Ae, Info) Debug.Print "X =", B Debug.Print "Info =", Info End Sub Example Results X = 2.09455148154233 Info = 0