numerically approximate the real roots of an expression using Newton's method - Maple Help

Online Help

All Products    Maple    MapleSim


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

Student[NumericalAnalysis][Newton] - numerically approximate the real roots of an expression using Newton's method

Calling Sequence

Newton(f, x=a, opts)

Newton(f, a, opts)

Parameters

f

-

algebraic; expression in the variable x representing a continuous function

x

-

name; the independent variable of f

a

-

numeric; the initial approximate root

opts

-

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

Description

• 

The Newton command numerically approximates the roots of an algebraic function, f, using the classical Newton-Raphson method.

• 

Given an expression f and an initial approximate a, the Newton 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. For sufficiently well-behaved functions and sufficiently good initial approximations, the convergence of pk toward the exact root is quadratic.

• 

The Newton command is a shortcut for calling the Roots command with the method=newton option.

Notes

• 

Newton's method will fail if xfpk1=0.ⅆⅆxfpk1=0

Examples

withStudent[NumericalAnalysis]:

f:=ⅇx+2x+2cosx6:

Newtonf,x=2.0,tolerance=102

1.829383715

(1)

Newtonf,x=2.0,tolerance=102,output=sequence

2.0,1.850521336,1.829751202,1.829383715

(2)

Newtonf,x=2,output=plot,stoppingcriterion=function_value

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.

Newtonf,x=1.3,output=animation,stoppingcriterion=absolute

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