The first two iterations of the secant method. The red curve shows the function f, and the blue lines are the secants. For this particular case, the secant method will not converge to the visible root.
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. However, the secant method predates Newton's method by over 3000 years.[1]
^Papakonstantinou, Joanna; Tapia, Richard (2013). "Origin and evolution of the secant method in one dimension". American Mathematical Monthly. 120 (6): 500–518. doi:10.4169/amer.math.monthly.120.06.500. JSTOR 10.4169/amer.math.monthly.120.06.500. S2CID 17645996 – via JSTOR.
the secantmethod 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...
of the cosine the secantmethod, a root-finding algorithm in numerical analysis, based on secant lines to graphs of functions a secant ogive in nose cone...
sufficiently well. The above formula is also used in the secantmethod, but the secantmethod always retains the last two computed points, and so, while...
performance. Popular alternatives to the bisection method, such as the secantmethod, Ridders' method or Brent's method (amongst others), typically perform better...
iteratively, either the secantmethod or the improved formula always converges to the correct solution. Both the secantmethod and the improved formula...
solution as K itself is a function of crack length. The other method, namely the secantmethod, uses the compliance-crack length equation given by ASTM standard...
derivative Secantmethod — based on linear interpolation at last two iterates False position method — secantmethod with ideas from the bisection method Muller's...
as can be proved by secantmethod analysis. As noted in the introduction, inverse quadratic interpolation is used in Brent's method. Inverse quadratic...
tangent functions. Their reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less used. Each of these six trigonometric...
ITP method, short for Interpolate Truncate and Project, is the first root-finding algorithm that achieves the superlinear convergence of the secant method...
however, that q {\displaystyle q} be an integer. For example, the secantmethod, when converging to a regular, simple root, has an order of φ ≈ 1.618...
For the intersecting secants theorem and chord theorem the power of a point plays the role of an invariant: Intersecting secants theorem: For a point...
(Fortran) SNOPT (Fortran) NLPQL (Fortran) MATLAB SuanShu (Java) Newton's methodSecantmethod Model Predictive Control Jorge Nocedal and Stephen J. Wright (2006)...
Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the...
S} and the interval reduced to [ 1 , 100 ] {\displaystyle [1,100]} , a secant line spanning the arc, or a tangent line somewhere along the arc may be...
within the class of quasi-Newton and multisecant methods, that generalize the well known secantmethod, for the solution of the non-linear equation g (...
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