% for a more readable version of this page.
%95/06/22: Cheney inquires about a formula for the max-norm of the cardinal B-spline, something he has been asked by his colleague, Jeremy Levesley, who has a contour integral for it. Cheney has an 8-line fortran program for it. %
I tell him that ter Morsche %
[%Morsche78
% tom
\refR Morsche, H. G. ter;
The minimum supremum norm of a B-spline;
T.H.-Report 78-WSK-05, Technological University Eindhoven; 1978;
]%
has looked at that, as have
%
[%MeinardusMorscheWalz95
Meinardus, G\"unther, Morsche, Hennie ter, Walz, Guido;
On the Chebyshev norm of polynomial $B$-splines;
\JAT; 82(1); 1995; 99--122;]
and that I remember some explicit statements there concerning this max-norm in
the cardinal case.
%
Of course, for large order,
%
Sommerfeld's
% asymptotic
expression for $B_n(x/(2h))$ provides the formula
$$%
\norm{B_n}_\infty \approx \sqrt{6/(\pi n)},
$$%
which gives the reasonable approximations, at $n=10, 100, 400$,
$$%
0.43701937223683,\ \ 0.13819765978853,\ \ 0.06909882989427,
$$%
for
$$%
0.43041776895944,\ \ 0.13799020407550,\ \ 0.06907291282945 .
$$%
\bye