The fastest algorithm to find the closest root of a strictly decreasing function is the Newton-Raphson Method, which does not require the explicit calculation of the derivative. If the derivative is available, Newton's tangent method is preferred; otherwise, the secant method can be utilized. The discussion emphasizes the importance of ensuring that the function value remains positive to a specified error margin, never dipping below zero. The implementation of a numerical derivative using a small delta value is also highlighted as a practical approach.
PREREQUISITESMathematicians, software developers, and engineers involved in numerical analysis, particularly those focused on root-finding algorithms for strictly decreasing functions.
dabd said:What is the fastest algorithm to find the closest root (such that the function value at that point is positive to an error but never negative, if not exactly zero) for a strictly decreasing function?
private static double df(double x) {
double del=0.000001;
double x0=f(x+del)-f(x);
x0=x0/del;
return x0;
}