numerically approximate the real roots of an expression using the secant method - Maple Help

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Student[NumericalAnalysis][Secant] - numerically approximate the real roots of an expression using the secant method

Calling Sequence

Secant(f, x=[a, b], opts)

Secant(f, [a, b], opts)

Parameters

f

-

algebraic; expression in the variable x representing a continuous function

x

-

name; the independent variable of f

a

-

numeric; one of two initial approximates to the root

b

-

numeric; the other of the two initial approximates to the root

opts

-

(optional) equation(s) of the form keyword=value, where keyword is one of functionoptions, lineoptions, maxiterations, output, pointoptions, showfunction, showlines, showpoints, showverticallines, stoppingcriterion, tickmarks, caption, tolerance, verticallineoptions, view; the options for approximating the roots of f

Description

• 

The Secant command numerically approximates the roots of an algebraic function, f, using a technique similar to Newton's method but without the need to evaluate the derivative of f.

• 

Given an expression f and an initial approximate a, the Secant command computes a sequence pk, k=0..n, of approximations to a root of f, where n is the number of iterations taken to reach a stopping criterion.

• 

The Secant command is a shortcut for calling the Roots command with the method=secant option.

Notes

• 

The secant method has the limitation that it may diverge when the initial approximates a and b are not sufficiently close to the root.

Examples

withStudent[NumericalAnalysis]:

f:=x37x2+14x6:

Secantf,x=2.7,3.2,tolerance=102

3.005775850

(1)

Secantf,x=2.7,3.2,tolerance=102,output=sequence

2.7,3.2,3.100884956,2.858406793,3.026267866,3.005775850

(2)

Secantf,x=2.7,3.2,tolerance=102,stoppingcriterion=absolute

2.999670283

(3)

To play the following animation in this help page, right-click (Control-click, on Macintosh) the plot to display the context menu.  Select Animation > Play.

Secantf,x=3.2,4.0,output=animation,stoppingcriterion=function_value

Secantf,x=2.9,3.1,tolerance=103,output=plot

See Also

Student[NumericalAnalysis], Student[NumericalAnalysis][Roots], Student[NumericalAnalysis][VisualizationOverview]


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