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

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Education : Student Package : Numerical Analysis : Visualization : Student/NumericalAnalysis/FalsePosition

Student[NumericalAnalysis][FalsePosition] - numerically approximate the real roots of an expression using the method of false position

Calling Sequence

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

FalsePosition(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 FalsePosition command numerically approximates the roots of an algebraic function, f, using a technique similar to the Secant method, but bracketing is incorporated.

• 

Given an expression f and an initial approximate a, the FalsePosition 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 FalsePosition command is a shortcut for calling the Roots command with the method=falseposition option.

Examples

withStudent[NumericalAnalysis]:

f:=x37x2+14x6:

FalsePositionf,x=2.7,3.2,tolerance=102

3.014898139

(1)

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

2.7,3.2,2.7,3.100884956,2.7,3.041032849,3.014898139

(2)

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

3.005163289

(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.

FalsePositionf,x=3.2,4.0,output=animation,tolerance=102,stoppingcriterion=function_value

FalsePositionf,x=2.9,3.1,output=plot

See Also

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


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam