This procedure computes the $L_{\mathrm{\infty }}$ (minimax) norm of a given real function f(x) on the interval [a, b]. Specifically, it computes an estimate for the value

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 $\left|f\left(x\right)\right|$ 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.

$\mathrm{with}\left(\mathrm{numapprox}\right)\:$

$\mathrm{infnorm}\left(\sin \,0..2\,'\mathrm{xmax}'\right)$

$1.0$

$\mathrm{xmax}$

$1.570796332$

$\mathrm{infnorm}\left(\frac{1}{\mathrm{\Gamma }\left(x\right)}\,x=1..2\right)$

$1.129173885$

$r\left[2,3\right]≔\mathrm{minimax}\left(\frac{\tan \left(x\right)}{x}\,x=0..\frac{\mathrm{\pi }}{4}\,\left[2\,3\right]\right)$

$r_{2,3}≔\frac{1.130422926+\left(-0.07842798254-0.07066118710x\right)x}{1.130423032+\left(-0.07843711579+\left(-0.4473405792+0.02547897687x\right)x\right)x}$

$\mathrm{infnorm}\left(\frac{\tan \left(x\right)}{x}-r\left[2,3\right]\,x=0..\frac{\mathrm{\pi }}{4}\,'\mathrm{xmax}'\right)$

$9.388658362\times {10}^{\mathrm{-8}}$

$\mathrm{xmax}$

$0.608882102369394$