Web Reference: Jul 15, 2025 ยท Secant method is a recursive method for finding the root of a polynomial by successive approximation. In this method, the neighborhood roots are approximated by secant line (A line that intersects the curve at two distinct points) to the function f (x). In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method, so it is considered a quasi-Newton method. By writing f (x) using the Taylor's expansion in the remainder form, we derive the superlinear convergence of the secant method. Two function evaluations of f (x) and f 0(x) per iteration while secant needs only one evaluation. Thus, secant is faster.
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