secant method

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secant method An iterative method for finding a root of the nonlinear equation f(x) = 0. It is given by the formula xn+2 = xn+1 – (xn+1xn)[f(xn+1)/(f(xn+1) – f(xn))] n = 0, 1, 2, …

where x0 and x1 are given starting values. This formula is derived by replacing f(x) by a straight line based on the last two iterates. Convergence is ultimately less rapid than for Newton's method, but it can be overall more efficient on some problems since derivatives are not required.