dfzero dfzero_r

dfzero() void dfzero ( double(*)(double)  f, double *  b, double *  c, double  r, double  re, double  ae, int *  info  ) Solution of a single general nonlinear equation Purpose dfzero 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: double f(double x) { return (computed function value f(x)); } [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: Normal return = 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)