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numapprox

  

infnorm

  

compute the L-infinity norm of a function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

infnorm(f, x=a..b, 'xmax')

infnorm(f, a..b, 'xmax')

Parameters

f

-

procedure or expression representing the function

x

-

variable name appearing in f, if f is an expression

a, b

-

numerical values specifying the interval [a, b]

xmax

-

(optional) name which will be assigned the point of maximum

Description

• 

This procedure computes the L (minimax) norm of a given real function f(x) on the interval [a, b]. Specifically, it computes an estimate for the value

maxfx,x∈a,b

• 

If the second argument is a range a..b then the first argument is understood to be a Maple operator. If the second argument is an equation x=a..b then the first argument is understood to be an expression in the variable x.

• 

If the third argument 'xmax' is present then it must be a name. Upon return, its value will be an estimate for the value of x where the maximum of fx is attained.

• 

Various levels of user information will be displayed during the computation if infolevel[infnorm] is assigned values between 1 and 4.

• 

The command with(numapprox,infnorm) allows the use of the abbreviated form of this command.

Examples

withnumapprox:

infnormsin,0..2,'xmax'

1.0

(1)

xmax

1.570796332

(2)

infnorm1Γx,x=1..2

1.129173885

(3)

r2,3minimaxtanxx,x=0..π4,2,3

r2,3:=1.130422926+0.078427982540.07066118710xx1.130423032+0.07843711579+0.4473405792+0.02547897687xxx

(4)

infnormtanxxr2,3,x=0..π4,'xmax'

9.38865836210-8

(5)

xmax

0.608882102369394

(6)

See Also

maximize

 


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