dfzero dfzero_r

dfzero_r() void dfzero_r ( double *  b, double *  c, double  r, double  re, double  ae, int *  info, double *  xx, double  yy, int *  irev  ) Solution of a single general nonlinear equation (reverse communication version) Purpose dfzero_r 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,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 [out] xx When returned with irev=1 to 4, xx contains the abscissa where the function value shoule be evaluated and given in the next call. [in] yy When returned with irev = 1 to 4, the function value f(xx) should be given in yy in the next call. [in,out] irev Control variable for reverse communication. [in] Before first call, irev should be initialized to zero. On succeeding calls, irev should not be altered. [out] If irev is not zero, complete the following process and call this routine again. = 0: Computation finished. See return code in info. = 1 to 4: User should set the function value at xx (f(xx)) in yy. Do not alter any variables other than yy. Reference D. Kahaner, C. Moler, S. Nash, "Numerical Methods and Software", Prentice-Hall (1989)