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Student[NumericalAnalysis]

  

RateOfConvergence

  

compute the rate of convergence of a sequence or function

 

Calling Sequence

Parameters

Options

Description

Examples

Calling Sequence

RateOfConvergence(S, n, opts)

Parameters

S

-

algebraic; the function or sequence

n

-

name; the name of the indexing variable

opts

-

(optional) equation(s) of the form keyword = value where keyword is isfunction; whether S is is a function or sequence

Options

• 

isfunction = true or false

  

Whether to find the rate of convergence of a sequence or a function.  If S is a function, isfunction must be set to true. By default, isfunction=false.

Description

• 

If the input is a sequence an, the return value of the RateOfConvergence command is of the form L+Ond, where L=limnan and anL=Ond for some 0<d.

• 

If the input is a function fx, the return value is of the form L+Oxd, where L=limx0fx and fxL=Oxd for some 0<d

• 

If S is a function, the option isfunction must be set to true.

• 

By default, the isfunction option is set to false.

Examples

withStudentNumericalAnalysis&colon;

RateOfConvergence1+1n&comma;n

1+O1n

(1)

RateOfConvergence121n2&comma;n

12+O1n2

(2)

RateOfConvergenceexpx&comma;x&comma;isfunction=true

1+Ox

(3)

See Also

Student[NumericalAnalysis]

Student[NumericalAnalysis][ComputationOverview]