My Math Forum QUick converging mimimization without derivatives?

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 March 27th, 2018, 11:40 AM #1 Newbie   Joined: Oct 2013 Posts: 20 Thanks: 0 QUick converging mimimization without derivatives? We have three points: $\displaystyle x_0, x+h$ and $\displaystyle x-h$. We interpolate parabola using Stirling formula. Next, x:=parabola extreme. We can much decrease h and have next 3 points:$\displaystyle x_0, x+h$ and $\displaystyle x-h$. One problem: fast decreasing accuracy because of zero in denominator. Code:  static double f(double x) { return (x - 1) * (x - 2) * (x - 3); } static void minparab(double x0,double h) { double kappa = 13.6; double xe = 1.4226497308103742355;//exact value for f(x) for (int i = 0; i < 10; i++) { double y0 = f(x0); double yp = f(x0 + h); double ym = f(x0 - h); double x = x0 + h * (0.25 * yp- 0.25 * ym) / (y0 - 0.5 *ym - 0.5 *yp); double hmin = Math.Abs(x - x0); if (hmin > h) h = hmin; double h2 = h * h / kappa; Console.WriteLine("{0}", x-xe); x0 = x; h = h2; } } static void test() { minparab(1.5, 0.1); }

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