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Secant method
  Applies the secant method to find a root of a nonlinear equation.
2024.May.17 12:27:02
x1, x2 Starting values (bracketing the root or not). •
par Parameters in function (see below). •
itmax, tol, monit Iterations (max.), tolerance, monitoring. •
Graph Graph of:  (f) function or (default) (i) iterations. •
Show values Shows the coordinates of the graph.

Applies the secant method to find the root (solution) of a nonlinear equation. The function (imbedded) is a polynomial, and only its parameters can be given. The base problem is thus y = 1 x3 - 1 x - 1 (user-given as 'par').

The method is defined by the following iterative procedure:  xn+1 = (yn.xn−1 − yn−1.xn) ⁄ (yn − yn−1), which —showing the relation to the Newton-Raphson method— can be written assecant.

A graph of y vs. var is made of: (f) the function (var = x); or (i) the iterations (var = i).

References: Plate: Secant

• Weisstein, Eric W., "Secant Method", from MathWorld —a Wolfram Web Resource.

• Chemistry Dept.: CH 490/590, Computer Programming for Scientists (Oregon State Univ.).

• Conte, Samuel D., Carl de Boor, 1987, "Elementary numerical analysis (an algorithmic approach)", 3.rd ed., McGraw-Hill. (ISBN 0-07-066228-2, p 78.)

• Conrad, Eric van Fossen: Latin phrases (Ohio State Univ.).

• 1888-01-08: Courant, Richard (1972-01-27).

 
 
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Created: 2009-01-08 — Last modified: 2010-11-07